Here's an interesting text by Fr. Sylvester E. Berry. How does this relate to our present situation? Pg. 267

"MAJORITY INFALLIBLE. Since the bishops are infallible in their corporate capacity only, individual bishops may err at any time in regard to faith and morals, but all cannot fall into the same error at the same time.

It seems most probable that the agreement of a majority is sufficient to insure the truth of any doctrine, for it would certainly be a great evil for the Church if the greater part of her teaching body could fall into error at any time.

VALUE OF TRADITION The value of Tradition as proof for revealed doctrine rests principally upon the active and passive infallibility [some writers call indefectibility as "passive infallibility"] of the Church. Whenever there are sufficient witnesses to prove that a certain doctrine is accepted by the whole Church as a revealed Truth, or that it is taught as such by a majority of the Bishops, it is immediately evident that the doctrine is infallibly true and could be defined as a a dogma of faith, if not already so defined. When appealing to Tradition in this sense, it matters not what age of the Church be selected, as truth does not change with the centuries. The truth of a doctrine is established just as securely by proving its universal acceptance today, as by showing that it was universally accepted in any past age of the Church."

Fr Berry acknowledges the objection.  He isn't going to acknowledge an objection from untrained laymen.  He is anticipating the objection of his theologian peers.  So it is a serious objection.  How does he answer it?  He basically says the bishops did not fail in faith, they just failed to meet the occasion.  But what was St Jerome's opinion?  "The whole world groaned in astonishment to find itself Arian".  (see Council of Rimini)

Objection II.  During the Arian heresy in the fourth century the Catholic Church ceased to be Catholic or universal, for, as St. Jerome said on one occasion: "The whole world groaned and was surprised to find itself Arian." ("Contra Luciferianos"; P.L., 23, 172.)

Answer. - These words of St. Jerome are not to be taken literally, as is evident from the circuмstances.  At the councils of Rimini and Selucia, in 359, the Arians gained a victory by having a creed adopted in which their errors were not directly condemned.  This aided them in the spread of their doctrines, because they could make it appear that the councils had approved them.  When hearing of this, St. Jerome used the words quoted in the objection. It is true that the Arians made rapid strides, even many priests and bishops fell into their errors, but the Church never ceased to be truly universal, and most probably continued at all times more wide-spread than the Arian sect, despite the fact that the emperors did all in their power to spread the heresy.  St. Athanasius and the bishops of his patriarchate wrote to the Emperor in this matter: "The churches of every nation agree with the Nicene Faith, - those in Spain, Britain, and Gaul; in Italy, Dalmatia, and Mysia; in Macedonia, in all Greece and the whole of Africa; in Sardinia, Cyprus, Crete, Pamphylia, Isauria, and Lycia, and in all Egypt and Lybia, Pontus, Cappadocia, and adjacent districts, and in all the eastern churches, except a few who believe with Arius.  We have certain knowledge regarding the above-mentioned  churches, because we have letters from them, and we know most religious Emperor, how few they are who contradict this faith." (St. Athanasius, "Ad Jovianum," quoted in Theordoret's Church History, IV, 3; P.G., 82, 1126.)

Even granting that these words contain some rhetorical exaggeration, they still show that the Church had not ceased to be truly Catholic by her diffusion through the then known world.

…Others again say that the Church has in fact failed, for errors have arisen, as if the power of a perverse will did not remain with man; and some urge that the whole Church has failed, quoting the expression of St. Jerome that, after the Council of Rimini in 359, the whole world found with surprise that it had fallen into the Arian heresy (Dial. adv. Luciferianos, n. 19; P.L. 23, 172), but not seeing that this phrase is merely a rhetorical or perhaps humorous exaggeration (see similar instances in Scripture, St. John xii. 19; xxi. 25), and whatever was the spirit of the remark, it certainly was not true, as may be seen by reference to the histories of the period. (See particularly Jungmann, Diss, in Hist. Eccles. vii.)

44. We now come back once more to the Arians. When Osius and Liberius fell, they were already split up into a great many sects: some who followed the party of Acasius, Eudoxius, Eunomius, and Aesius, were called Anomeans—those were pure Arians, and they not alone rejected consubstantiality, but even the likeness of the Son to the Father; but the followers of Ursacius and Valens, though called Arians, did not follow' the opinions of Arius in everything. Finally, those who followed the opinions of Basil of Ancyra, and Eustatius of Sebaste, were called Semi-Arians; these condemned the blasphemies of Arius, but did not admit the consubstantiality of the divine persons (12).

45. We have now to relate the events of the Council of Rimini, of sorrowful celebrity, in which, as St. Jerome says, the Nicene faith was condemned, and the whole world groaned, finding itself Arian. When the whole Church was in confusion about the articles of the faith, it was considered that the best way of arranging everything quietly, would be to hold two councils, one in Rimini in Italy, the other at Seleucia in the East. The Council of Rimini was held in 359, and was attended by more than four hundred bishops from Illyria, Italy, Africa, Spain, Gaul, and Britain, and among those there were eighty Arians, but the rest were Catholic. When they came to treat of matters of faith, Ursacius, Valens, and other heads of the Arian party produced a writing, and proposed that all should be satisfied with signing that, in which was laid down the last formula of Sirmium of the same year, in which, it is true, the word substance was rejected, but it was allowed that the Son was like unto the Father in all things. But the Catholic bishops unanimously answered that there was no necessity for any other formula, but that of the Council of Nice, and decreed that there should be no addition to or subtraction from that formula; that the word substance should be retained, and they again condemned the doctrine of Arius, and published ten anathemas against the errors of Arius, Sabellius, and Photinus. All the Catholics subscribed to this, but Ursacius. Valens and the Arians refused, so they themselves were judged heretics, and Ursacius, Valens, Caius, and Germinius were condemned and deposed by a formal act (13).

46. Ten bishops were now sent as legates from the council to the Emperor, bearers of the letters of the council, giving him notice that the fathers had decided that there should be nothing added to or taken from the Council of Nice, and that they regretted to find that Ursacius and Valens wished to establish another formula of faith, according to the docuмent they presented to the council. The ten legates accordingly went, but the Arians sent ten likewise, along with Ursacius and Valens, and these arrived first and prejudiced the Emperor against the council, and presented him with the formula of Sirmium, which was rejected by the Council of Rimini. When the legates sent by the council arrived, they could not obtain an audience from the Emperor, and it was only after a long delay, that he sent an answer to the council, that he was about to proceed against the barbarians, and that he had given orders to the legates to wait for him in Adrianople, where he would see them on his return, and give them his final answer. The fathers of the council wrote again to Constantius, telling him that nothing would ever change them, and begging therefore that he would give an audience to the legates and let them depart. When the Emperor came to Adrianople, the legates followed him, and were taken to the small town of Nice, in the neighbourhood; and there they began to treat with the Arians against the express orders of the council, which particularly restricted them on this point. Partly by deception, and partly by threats, they were induced to sign a formula, worse even than the third formula of Sirmium; for not only was the word substance omitted, but the Son was said to be like unto the Father, but leaving out in all things, which was admitted in the Sirmium formula. They were, likewise, induced to revoke the deposition of Ursacius, and his companions, condemned by the council; and they signed the formula with their own hands (14).

47. The legates having put things in this state returned to Rimini, and Constantius then gave orders to his Prefect Taurus, not to permit the council to be dissolved, till the bishops had signed the last formula of Nice, and to send into banishment any bishops refusing their signature, if their number did not exceed fifteen. He likewise wrote a letter to the fathers of the council, prohibiting them from using the words substantial and consubstantial. Ursacius and Valens now returned to Rimini, and as their party was now in the ascendant, they seized on the church, and wrote to the Emperor that he was obeyed, arid that the expressions he objected to were not allowed to be used any more. The Catholics, at first, made a show of constancy, and refused to communicate with the legates, who excused their error by alleging all they suffered at the Court of the Emperor; but by degrees they were tired out, their constancy failed, and they subscribed the same formula as the legates (15).

48. We cannot deny but that the bishops of Rimini committed a great error, but they are not so much to be blamed for bad faith, as for not being more guarded against the wiles of the Arians. This was the snare that was laid for them:—They were wavering as to whether they should sign the formula or not, and when they were all assembled in the church, and the errors attributed to Valens, who drew up the formula, were read out, he protested that he was not an Arian. "Let him be excommunicated," he exclaimed, " who asserts that Jesus Christ is not the Son of God, born of the Father before all ages. Let him be excommunicated who says that he is not like unto the Father, according to the Scriptures; or, he who says he is a creature like all other creatures —(how he conceals the poison, for he taught that Christ was a creature, but more perfect than all the others);—or that he is from nothing, and not from the Father; or that there was a time when he was not; or that anything was before him;—he who teaches any of those things let him be excommunicated." And all answered:—"Let him be excommunicated." These denunciations of anathema, so fraudulently put forward, threw the Catholics off their guard. They persuaded themselves that Valens was not an Arian, and were induced to sign the formula; and thus the Council of Rimini, which opened so gloriously, was ignominiously terminated, and the bishops got leave to return to their homes. They were not long, St. Jerome tells us, till they discovered their error; for the Arians, immediately on the dissolution of the council, began to boast of their victory. The word substantial, said they, is now abolished, and along with it the Nicene faith; and when it was said, that the Son was not a creature, the meaning was, that he was not like the other created beings, but of a higher order, and then it was that the world, St. Jerome says, groaning, found itself Arian. Noel Alexander proves, from St. Jerome, St. Ambrose, and others, and with very convincing arguments, too, that the bishops of Rimini, in subscribing that formula, did not violate the faith; for, taken in its obvious sense, it contained nothing heretical. While the Council of Rimini was in progress, there was another council held in Seleucia, at which many Arian bishops were present; but it was soon dismissed, for the bishops were so divided, that they could not agree to any formula (16).

49. After the Council of Rimini was dissolved, the Arians of Antioch, in the year 361, not satisfied with the formula adopted at the council, drew up another in which they said, that the Son was in everything unlike the Father, not alone in substance, but also in will, and that he was formed out of nothing, as Arius had already taught. Fleury counts sixteen formulas published by the Arians. Liberius, however, after his first error in subscribing the formula of Sirmium, as we have already related (No. 41), constantly refused, after his liberation in 360, to sign the formula of Rimini, and, as Baronius relates in his Acts of Pope Liberius, he was obliged to leave Rome and hide himself in the catacombs, where Damasus and the rest of his clergy went to see him, and he remained there until the death of Constantius in 361. St. Gregory of nαzιanzen says that Constantius, just before his death, repented, but in vain, of three things:—Of the murder of his relatives; of having made Julian, Caesar; and of causing such confusion in the Church. He died, however, in the arms of the Arians, whom he protected with such zeal, and Euzoius, whom he had made Bishop of Antioch, administered him baptism just before his death. His death put an end to the synods, and for a time restored peace to the Church; as St. Jerome says, "The beast dies and the calm returns" (17).

(12) N. Alex. t. 9; Hermant. t. 1, c.102. 

(13) S. Hieron., Dialog., ad Lncifer. Fleury, t. 2. Orsi, cit. S. Athan. tie Synod. Sozymen, I. 2.

(14) Theod. 1. 2, c. 19; Soz. l. 4; Soc . /. 2. 

(15) St Hila. Fragmen. p. 453, Sulp. Ser. I . 2. 

(16) S. Hieron. ad. Ludf. n. 17; Nat., Fleury, & Orsi, loc . con.; N. Alex. Die. 33, I . 9.

(17) Baron. An. 359; St. Athan. de Synod.; Fleury, I. 14, n. 33; St. Greg. Naz. Oral. 21; Soc . I . 2, c. 47.