This subject has been examined by the Church over the centuries in great detail.  I would suggest you start with Questions 98 through 108 of St. Thomas Aquinas' Summa Theologica (Prima Secundæ Partis), which examine the Old Law and its relationship to the New Law.  One translation can be found here:  http://www.newadvent.org/summa/2.htm.

With this in mind, it seems to me that many of the mosaic laws, that were not fulfilled by Jesus Christ, still apply.

Nothing of the Old Law was left unfulfilled by Our Lord. What aspect of the Mosaic Law could possibly not have been sufficiently fulfilled by the Sacrafice of Calvary, which was the very Event that all of the Old Law was designed to point toward?

I'm also considering that these laws may only apply to those descended of the Israelites since they were a covenant between God and the Israelites only.

Am I wrong?

Yes. Exceedingly so.

Look to how the Church, through the Inquisition, dealt with the Marranos, who were doing just what you're suggesting here.

As Ladislaus says, the abolishment of the Mosaic Law is de Fide. The continued practice of Mosaic dietary restrictions among Catholics of Jєωιѕн stock in the Patriarchate of Jerusalem in the first and second centuries (which, amazingly, still survives as one of the many corrupt and degenerate practices of the backwards Eritrean schismatics) was merely a disciplinary expediency respecting long held cultural practices for the sake of unity.  If you find yourself running afoul of any putative "Catholics" calling for a return to this practice, get as far away from them as you can. We ought to know better than anyone the disastrous results of liturgical and disciplinary primativism, especially when it's put in service of an "ecuмenical" (read: Judaizing) agenda.

Quote from: Council of Florence

[The Sacrosanct Roman Church] ... firmly believes, professes, and teaches that the matter pertaining to the law of the Old Testament, of the Mosiac law, which are divided into ceremonies, sacred rites, sacrifices, and sacraments, because they were established to signify something in the future, although they were suited to the divine worship at that time, after our Lord's coming had been signified by them, ceased, and the sacraments of the New Testament began; and that whoever, even after the passion, placed hope in these matters of the law and submitted himself to them as necessary for salvation, as if faith in Christ could not save without them, sinned mortally. Yet it does not deny that after the passion of Christ up to the promulgation of the Gospel they could have been observed until they were believed to be in no way necessary for salvation; but after the promulgation of the Gospel it asserts that they cannot be observed without the loss of eternal salvation. All, therefore, who after that time observe circuмcision and the Sabbath and the other requirements of the law, it declares alien to the Christian faith and not in the least fit to participate in eternal salvation, unless someday they recover from these errors. Therefore, it commands all who glory in the name of Christian, at whatever time, before or after baptism' to cease entirely from circuмcision, since, whether or not one places hope in it, it cannot be observed at all without the loss of eternal salvation.

Here you go.

I do wonder about this though:  "Therefore, it commands all who glory in the name of Christian, at whatever time, before or after baptism' to cease entirely from circuмcision, since, whether or not one places hope in it, it cannot be observed at all without the loss of eternal salvation."  I thought it was OK to do circuмcision for hygenic (non-religious reason).  Perhaps the key is the word "observed", i.e. doing it in the sense of a ritual vs. medically for hygenic reasons.

Unfortunately, I was conned into believing the "hygenic" bunk and had my first son circuмcised. Thanks be to God, we were able to spare our second little boy from this now totally unnecessary procedure.

Quote from: InfiniteFaith

With this in mind, it seems to me that many of the mosaic laws, that were not fulfilled by Jesus Christ, still apply.

Nothing of the Old Law was left unfulfilled by Our Lord. What aspect of the Mosaic Law could possibly not have been sufficiently fulfilled by the Sacrafice of Calvary, which was the very Event that all of the Old Law was designed to point toward?

Quote from: InfiniteFaith

I'm also considering that these laws may only apply to those descended of the Israelites since they were a covenant between God and the Israelites only.

Am I wrong?

Yes. Exceedingly so.

Look to how the Church, through the Inquisition, dealt with the Marranos, who were doing just what you're suggesting here.

As Ladislaus says, the abolishment of the Mosaic Law is de Fide. The continued practice of Mosaic dietary restrictions among Catholics of Jєωιѕн stock in the Patriarchate of Jerusalem in the first and second centuries (which, amazingly, still survives as one of the many corrupt and degenerate practices of the backwards Eritrean schismatics) was merely a disciplinary expediency respecting long held cultural practices for the sake of unity.  If you find yourself running afoul of any putative "Catholics" calling for a return to this practice, get as far away from them as you can. We ought to know better than anyone the disastrous results of liturgical and disciplinary primativism, especially when it's put in service of an "ecuмenical" (read: Judaizing) agenda.

I was thinking about these particular types of mosaic laws:

Not to reap the entire field (Lev. 19:9; Lev. 23:22)
To leave the unreaped corner of the field or orchard for the poor (Lev. 19:9)
Not to gather ol'loth (the imperfect clusters) of the vineyard (Lev. 19:10)
To leave ol'loth (the imperfect clusters) of the vineyard for the poor (Lev. 19:10; Deut. 24:21) (affirmative) (CCI3).
Not to gather the peret (grapes) that have fallen to the ground (Lev. 19:10) (negative) (CCI9).
To leave peret (the single grapes) of the vineyard for the poor (Lev. 19:10) (affirmative) (CCI4).
Not to return to take a forgotten sheaf (Deut. 24:19) This applies to all fruit trees (Deut. 24:20) (negative) (CC10).
To leave the forgotten sheaves for the poor (Deut. 24:19-20)

How might you explain Christ fulfilling these?

It's de fide that the Mosaic Law has been abolished.

Yes, the matter has already been infallibly settled:

The Catholic Church firmly believes, professes, and teaches that the matter pertaining to the law of the Old Testament, of the Mosaic law, which are divided into ceremonies, sacred rites, sacrifices, and sacraments, because they were established to signify something in the future, although they were suited to the divine worship at that time, after our Lord’s coming had been signified by them, ceased, and the sacraments of the New Testament began; and that whoever, even after the passion, placed hope in these matters of the law and submitted himself to them as necessary for salvation, as if faith in Christ could not save without them, sinned mortally. Yet it does not deny that after the passion of Christ up to the promulgation of the Gospel they could have been observed until they were believed to be in no way necessary for salvation; but after the promulgation of the Gospel it asserts that they cannot be observed without the loss of eternal salvation. All, therefore, who after that time observe circuмcision and the Sabbath and the other requirements of the law, it declares alien to the Christian faith and not in the least fit to participate in eternal salvation, unless someday they recover from these errors.” (Denz. 712)

The passage above is founded upon the teachings of St. Aquinas in the Summa as Dolores pointed out. After the promulgation of the Gospel, it has always been considered as mortally sinful for a Catholic to practice Jєωιѕн rites.

This should held you a bit, IF:

Summa Theologica[/i], Prima Secundæ Partis, Question 103]Article 4. Whether since Christ's Passion the legal ceremonies can be observed without committing mortal sin?

Objection 1. It would seem that since Christ's Passion the legal ceremonies can be observed without committing mortal sin. For we must not believe that the apostles committed mortal sin after receiving the Holy Ghost: since by His fulness they were "endued with power from on high" (Luke 24:49). But the apostles observed the legal ceremonies after the coming of the Holy Ghost: for it is stated (Acts 16:3) that Paul circuмcised Timothy: and (Acts 21:26) that Paul, at the advice of James, "took the men, and . . . being purified with them, entered into the temple, giving notice of the accomplishment of the days of purification, until an oblation should be offered for every one of them." Therefore the legal ceremonies can be observed since the Passion of Christ without mortal sin.

Objection 2. Further, one of the legal ceremonies consisted in shunning the fellowship of Gentiles. But the first Pastor of the Church complied with this observance; for it is stated (Galatians 2:12) that, "when" certain men "had come" to Antioch, Peter "withdrew and separated himself" from the Gentiles. Therefore the legal ceremonies can be observed since Christ's Passion without committing mortal sin.

Objection 3. Further, the commands of the apostles did not lead men into sin. But it was commanded by apostolic decree that the Gentiles should observe certain ceremonies of the Law: for it is written (Acts 15:28-29): "It hath seemed good to the Holy Ghost and to us, to lay no further burden upon you than these necessary things: that you abstain from things sacrificed to idols, and from blood, and from things strangled, and from fornication." Therefore the legal ceremonies can be observed since Christ's Passion without committing mortal sin.

On the contrary, The Apostle says (Galatians 5:2): "If you be circuмcised, Christ shall profit you nothing." But nothing save mortal sin hinders us from receiving Christ's fruit. Therefore since Christ's Passion it is a mortal sin to be circuмcised, or to observe the other legal ceremonies.

I answer that, All ceremonies are professions of faith, in which the interior worship of God consists. Now man can make profession of his inward faith, by deeds as well as by words: and in either profession, if he make a false declaration, he sins mortally. Now, though our faith in Christ is the same as that of the fathers of old; yet, since they came before Christ, whereas we come after Him, the same faith is expressed in different words, by us and by them. For by them was it said: "Behold a virgin shall conceive and bear a son," where the verbs are in the future tense: whereas we express the same by means of verbs in the past tense, and say that she "conceived and bore." In like manner the ceremonies of the Old Law betokened Christ as having yet to be born and to suffer: whereas our sacraments signify Him as already born and having suffered. Consequently, just as it would be a mortal sin now for anyone, in making a profession of faith, to say that Christ is yet to be born, which the fathers of old said devoutly and truthfully; so too it would be a mortal sin now to observe those ceremonies which the fathers of old fulfilled with devotion and fidelity. Such is the teaching Augustine (Contra Faust. xix, 16), who says: "It is no longer promised that He shall be born, shall suffer and rise again, truths of which their sacraments were a kind of image: but it is declared that He is already born, has suffered and risen again; of which our sacraments, in which Christians share, are the actual representation."

Reply to Objection 1. On this point there seems to have been a difference of opinion between Jerome and Augustine. For Jerome (Super Galat. ii, 11, seqq.) distinguished two periods of time. One was the time previous to Christ's Passion, during which the legal ceremonies were neither dead, since they were obligatory, and did expiate in their own fashion; nor deadly, because it was not sinful to observe them. But immediately after Christ's Passion they began to be not only dead, so as no longer to be either effectual or binding; but also deadly, so that whoever observed them was guilty of mortal sin. Hence he maintained that after the Passion the apostles never observed the legal ceremonies in real earnest; but only by a kind of pious pretense, lest, to wit, they should scandalize the Jєωs and hinder their conversion. This pretense, however, is to be understood, not as though they did not in reality perform those actions, but in the sense that they performed them without the mind to observe the ceremonies of the Law: thus a man might cut away his foreskin for health's sake, not with the intention of observing legal circuмcision.

But since it seems unbecoming that the apostles, in order to avoid scandal, should have hidden things pertaining to the truth of life and doctrine, and that they should have made use of pretense, in things pertaining to the salvation of the faithful; therefore Augustine (Epist. lxxxii) more fittingly distinguished three periods of time. One was the time that preceded the Passion of Christ, during which the legal ceremonies were neither deadly nor dead: another period was after the publication of the Gospel, during which the legal ceremonies are both dead and deadly. The third is a middle period, viz. from the Passion of Christ until the publication of the Gospel, during which the legal ceremonies were dead indeed, because they had neither effect nor binding force; but were not deadly, because it was lawful for the Jєωιѕн converts to Christianity to observe them, provided they did not put their trust in them so as to hold them to be necessary unto salvation, as though faith in Christ could not justify without the legal observances. On the other hand, there was no reason why those who were converted from heathendom to Christianity should observe them. Hence Paul circuмcised Timothy, who was born of a Jєωιѕн mother; but was unwilling to circuмcise Titus, who was of heathen nationality.

The reason why the Holy Ghost did not wish the converted Jєωs to be debarred at once from observing the legal ceremonies, while converted heathens were forbidden to observe the rites of heathendom, was in order to show that there is a difference between these rites. For heathenish ceremonial was rejected as absolutely unlawful, and as prohibited by God for all time; whereas the legal ceremonial ceased as being fulfilled through Christ's Passion, being instituted by God as a figure of Christ.

Reply to Objection 2. According to Jerome, Peter withdrew himself from the Gentiles by pretense, in order to avoid giving scandal to the Jєωs, of whom he was the Apostle. Hence he did not sin at all in acting thus. On the other hand, Paul in like manner made a pretense of blaming him, in order to avoid scandalizing the Gentiles, whose Apostle he was. But Augustine disapproves of this solution: because in the canonical Scripture (viz. Galatians 2:11), wherein we must not hold anything to be false, Paul says that Peter "was to be blamed." Consequently it is true that Peter was at fault: and Paul blamed him in very truth and not with pretense. Peter, however, did not sin, by observing the legal ceremonial for the time being; because this was lawful for him who was a converted Jєω. But he did sin by excessive minuteness in the observance of the legal rites lest he should scandalize the Jєωs, the result being that he gave scandal to the Gentiles.

Reply to Objection 3. Some have held that this prohibition of the apostles is not to be taken literally, but spiritually: namely, that the prohibition of blood signifies the prohibition of murder; the prohibition of things strangled, that of violence and rapine; the prohibition of things offered to idols, that of idolatry; while fornication is forbidden as being evil in itself: which opinion they gathered from certain glosses, which expound these prohibitions in a mystical sense. Since, however, murder and rapine were held to be unlawful even by the Gentiles, there would have been no need to give this special commandment to those who were converted to Christ from heathendom. Hence others maintain that those foods were forbidden literally, not to prevent the observance of legal ceremonies, but in order to prevent gluttony. Thus Jerome says on Ezekiel 44:31 ("The priest shall not eat of anything that is dead"): "He condemns those priests who from gluttony did not keep these precepts."

But since certain foods are more delicate than these and more conducive to gluttony, there seems no reason why these should have been forbidden more than the others.

We must therefore follow the third opinion, and hold that these foods were forbidden literally, not with the purpose of enforcing compliance with the legal ceremonies, but in order to further the union of Gentiles and Jєωs living side by side. Because blood and things strangled were loathsome to the Jєωs by ancient custom; while the Jєωs might have suspected the Gentiles of relapse into idolatry if the latter had partaken of things offered to idols. Hence these things were prohibited for the time being, during which the Gentiles and Jєωs were to become united together. But as time went on, with the lapse of the cause, the effect lapsed also, when the truth of the Gospel teaching was divulged, wherein Our Lord taught that "not that which entereth into the mouth defileth a man" (Matthew 15:11); and that "nothing is to be rejected that is received with thanksgiving" (1 Timothy 4:4). With regard to fornication a special prohibition was made, because the Gentiles did not hold it to be sinful.

Summa Theologica[/i], Prima Secundæ Partis, Question 107]Article 2. Whether the New Law fulfils the Old?

Objection 1. It would seem that the New Law does not fulfil the Old. Because to fulfil and to void are contrary. But the New Law voids or excludes the observances of the Old Law: for the Apostle says (Galatians 5:2): "If you be circuмcised, Christ shall profit you nothing." Therefore the New Law is not a fulfilment of the Old.

Objection 2. Further, one contrary is not the fulfilment of another. But Our Lord propounded in the New Law precepts that were contrary to precepts of the Old Law. For we read (Matthew 5:27-32): You have heard that it was said to them of old: . . . "Whosoever shall put away his wife, let him give her a bill of divorce. But I say to you that whosoever shall put away his wife . . . maketh her to commit adultery." Furthermore, the same evidently applies to the prohibition against swearing, against retaliation, and against hating one's enemies. In like manner Our Lord seems to have done away with the precepts of the Old Law relating to the different kinds of foods (Matthew 15:11): "Not that which goeth into the mouth defileth the man: but what cometh out of the mouth, this defileth a man." Therefore the New Law is not a fulfilment of the Old.

Objection 3. Further, whoever acts against a law does not fulfil the law. But Christ in certain cases acted against the Law. For He touched the leper (Matthew 8:3), which was contrary to the Law. Likewise He seems to have frequently broken the sabbath; since the Jєωs used to say of Him (John 9:16): "This man is not of God, who keepeth not the sabbath." Therefore Christ did not fulfil the Law: and so the New Law given by Christ is not a fulfilment of the Old.

Objection 4. Further, the Old Law contained precepts, moral, ceremonial, and judicial, as stated above (Question 99, Article 4). But Our Lord (Matthew 5) fulfilled the Law in some respects, but without mentioning the judicial and ceremonial precepts. Therefore it seems that the New Law is not a complete fulfilment of the Old.

On the contrary, Our Lord said (Matthew 5:17): "I am not come to destroy, but to fulfil": and went on to say (Matthew 5:18): "One jot or one tittle shall not pass of the Law till all be fulfilled."

I answer that, As stated above (Article 1), the New Law is compared to the Old as the perfect to the imperfect. Now everything perfect fulfils that which is lacking in the imperfect. And accordingly the New Law fulfils the Old by supplying that which was lacking in the Old Law.

Now two things of every law is to make men righteous and virtuous, as was stated above (Question 92, Article 1): and consequently the end of the Old Law was the justification of men. The Law, however, could not accomplish this: but foreshadowed it by certain ceremonial actions, and promised it in words. And in this respect, the New Law fulfils the Old by justifying men through the power of Christ's Passion. This is what the Apostle says (Romans 8:3-4): "What the Law could not do . . . God sending His own Son in the likeness of sinful flesh . . . hath condemned sin in the flesh, that the justification of the Law might be fulfilled in us." And in this respect, the New Law gives what the Old Law promised, according to 2 Corinthians 1:20: "Whatever are the promises of God, in Him," i.e. in Christ, "they are 'Yea'." [The Douay version reads thus: "All the promises of God are in Him, 'It is'."] Again, in this respect, it also fulfils what the Old Law foreshadowed. Hence it is written (Colossians 2:17) concerning the ceremonial precepts that they were "a shadow of things to come, but the body is of Christ"; in other words, the reality is found in Christ. Wherefore the New Law is called the law of reality; whereas the Old Law is called the law of shadow or of figure.

Now Christ fulfilled the precepts of the Old Law both in His works and in His doctrine. In His works, because He was willing to be circuмcised and to fulfil the other legal observances, which were binding for the time being; according to Galatians 4:4: "Made under the Law." In His doctrine He fulfilled the precepts of the Law in three ways. First, by explaining the true sense of the Law. This is clear in the case of murder and adultery, the prohibition of which the Scribes and Pharisees thought to refer only to the exterior act: wherefore Our Lord fulfilled the Law by showing that the prohibition extended also to the interior acts of sins. Secondly, Our Lord fulfilled the precepts of the Law by prescribing the safest way of complying with the statutes of the Old Law. Thus the Old Law forbade perjury: and this is more safely avoided, by abstaining altogether from swearing, save in cases of urgency. Thirdly, Our Lord fulfilled the precepts of the Law, by adding some counsels of perfection: this is clearly seen in Matthew 19:21, where Our Lord said to the man who affirmed that he had kept all the precepts of the Old Law: "One thing is wanting to thee: If thou wilt be perfect, go, sell whatsoever thou hast," etc. [St. Thomas combines Matthew 19:21 with Mark 10:21.

Reply to Objection 1. The New Law does not void observance of the Old Law except in the point of ceremonial precepts, as stated above (13, 3,4). Now the latter were figurative of something to come. Wherefore from the very fact that the ceremonial precepts were fulfilled when those things were accomplished which they foreshadowed, it follows that they are no longer to be observed: for it they were to be observed, this would mean that something is still to be accomplished and is not yet fulfilled. Thus the promise of a future gift holds no longer when it has been fulfilled by the presentation of the gift. In this way the legal ceremonies are abolished by being fulfilled.

Reply to Objection 2. As Augustine says (Contra Faust. xix, 26), those precepts of Our Lord are not contrary to the precepts of the Old Law. For what Our Lord commanded about a man not putting away his wife, is not contrary to what the Law prescribed. "For the Law did not say: 'Let him that wills, put his wife away': the contrary of which would be not to put her away. On the contrary, the Law was unwilling that a man should put away his wife, since it prescribed a delay, so that excessive eagerness for divorce might cease through being weakened during the writing of the bill. Hence Our Lord, in order to impress the fact that a wife ought not easily to be put away, allowed no exception save in the case of fornication." The same applies to the prohibition about swearing, as stated above. The same is also clear with respect to the prohibition of retaliation. For the Law fixed a limit to revenge, by forbidding men to seek vengeance unreasonably: whereas Our Lord deprived them of vengeance more completely by commanding them to abstain from it altogether. With regard to the hatred of one's enemies, He dispelled the false interpretation of the Pharisees, by admonishing us to hate, not the person, but his sin. As to discriminating between various foods, which was a ceremonial matter, Our Lord did not forbid this to be observed: but He showed that no foods are naturally unclean, but only in token of something else, as stated above (102, 6, ad 1).

Reply to Objection 3. It was forbidden by the Law to touch a leper; because by doing so, man incurred a certain uncleanness of irregularity, as also by touching the dead, as stated above (102, 5, ad 4). But Our Lord, Who healed the leper, could not contract an uncleanness. By those things which He did on the sabbath, He did not break the sabbath in reality, as the Master Himself shows in the Gospel: both because He worked miracles by His Divine power, which is ever active among things; and because He worked miracles by His Divine power, which is ever active among things; and because His works were concerned with the salvation of man, while the Pharisees were concerned for the well-being of animals even on the sabbath; and again because on account of urgency He excused His disciples for gathering the ears of corn on the sabbath. But He did seem to break the sabbath according to the superstitious interpretation of the Pharisees, who thought that man ought to abstain from doing even works of kindness on the sabbath; which was contrary to the intention of the Law.

Reply to Objection 4. The reason why the ceremonial precepts of the Law are not mentioned in Matthew 5 is because, as stated above (ad 1), their observance was abolished by their fulfilment. But of the judicial precepts He mentioned that of retaliation: so that what He said about it should refer to all the others. With regard to this precept, He taught that the intention of the Law was that retaliation should be sought out of love of justice, and not as a punishment out of revengeful spite, which He forbade, admonishing man to be ready to suffer yet greater insults; and this remains still in the New Law.

Ladislaus - that circuмcision condemnation is definitely suspect.  Because, what are we then to make of st. paul circuмcising st. timothy in order to preach to the Jєωs?  

I think that he did this for tactical reasons.  Otherwise, he would have been in no position to rebuke St. Peter for doing something similar.