It is in no way a contradiction. The teachings of the Pope are part of the Ordinary Magisterium, but they are not infallible unless they are ex cathedra. Therefore, the rest of it is fallible and can be wrong. So the Pope, and therefore the Ordinary(but not Universal) Magisterium can teach in error. It's fallible.  But it's infallibly safe in that you can never be guilty of sin for giving religious assent to the teachings of the Pope, even if they later turn out to be wrong.

It's even slightly more than that.  Even if a non-infallible teaching on one matter or another might be mistaken with regard to some details, accepting it and submitting to it cannot harm or endanger one's faith in any substantial way.  So, for instance, let's say, for the sake of argument, that the Church had been wrong in condemning heliocentrism (cassini, don't come out guns a blazing, since I don't believe that the Church was wrong about that), would it have done any harm to one's faith to believe in geocentrism?  Of course not.

Here's Msgr. Fenton regarding infallible safety (he's treating specifically of Encyclicals but the principles apply more broadly):

...God has given the Holy Father a kind of infallibility distinct from the charism of doctrinal infallibility in the strict sense. He has so constructed and ordered the Church that those who follow the directives given to the entire kingdom of God on earth will never be brought into the position of ruining themselves spiritually through this obedience. Our Lord dwells within His Church in such a way that those who obey disciplinary and doctrinal directives of this society can never find themselves displeasing God through their adherence to the teachings and the commands given to the universal Church militant. Hence there can be no valid reason to discountenance even the non-infallible teaching authority of Christ’s vicar on earth.
...
It is, of course, possible that the Church might come to modify its stand on some detail of teaching presented as non-infallible matter in a papal encyclical. The nature of the auctoritas providentiae doctrinalis within the Church is such, however, that this fallibility extends to questions of relatively minute detail or of particular application. The body of doctrine on the rights and duties of labor, on the Church and State, or on any other subject treated extensively in a series of papal letters directed to and normative for the entire Church militant could not be radically or completely erroneous. The infallible security Christ wills that His disciples should enjoy within His Church is utterly incompatible with such a possibility.

Stubborn just lambasted me and basically accused me of heresy and insulting the Body of Christ for saying that the Ordinary Magisterium is fallible - when his entire (correct) argument just before that was that only a specific portion of the Magisterium is fallible. Throwing around insults because he can't see the contradictions in his own posts.

Stubborn has his own definition of Magisterium which excludes the non-infallible portions of Church teaching.  I've pointed out to him that it's a semantic disagreement and that he's not using the term Magisterium in the same way that most Catholic theologians do.  Within the authentic Magisterium, theolgians distinguish between the mere authenticuм ("merely authentic" = non-infallible) and then the infallible Magisterium.

You are correct that most even Traditional Catholics don't make the proper distinctions between Ordinary (merely-authentic), Ordinary Universal, and Extraordinary.  In addition to that, sometimes you have the Pope speaking as a private doctor.

I personally hold another category.  When the Pope writes a letter to a Bishop, which has happened many times, he is in fact teaching/instructing the bishop as Pope, in his official capacity, but he is not addressing a teaching to the Universal Church.  Or when he gives a speech to a group of midwives.  He is speaking to them as Pope, but the scope of his teaching is too narrow to make it strictly part of the Magisterium.  Or when he would give a sermon at Sunday Mass.  So that is a category somewhere between teaching as a private doctor and exercising Magisterium towards the Universal Church.

You're the one who's been arguing that the Magisterium can be wrong. As you said so yourself, not even all the Bishops and the Pope being in agreement makes something infallible. It must always be something the Church has always taught. Therefore, by your own logic, the rest of the Ordinary Magisterium must be fallible. Stop flip-flopping.

Try to tell the guy something and look what he says. How on God's green earth could you possibly come up with that from my posts?

Just stop parroting that the Magisterium, being infallibly safe, can be wrong, but not too wrong! Such an amazing bit of theological wizadry on your part - and others.

So now go ahead, you or anyone, and provide some examples of the Magisterium being wrong, and also when it is wrong "but it can't lead you into heresy or rejection of the faith".

I know you're avoiding providing even a single example because it is an impossibility, but your pride must be stopping you from admitting it, but give it a shot any way.

I had this battle with him for a long time, and I discovered, at long last, that he was not in fact contradicting himself, but, rather, defining terms differently than most Catholic theologians.  Non-infallible teachings made by the Pope that happen to be wrong he would say are not actually part of the Magisterium (as he defines it).

The pope is not the magisterium. It is so obvious why you think he is, but he is not, neither is the hierarchy the magisterium. The magisterium is teachings, not people.

Why would you think that I believe this when you were on the thread where I called out XavierSem for conflating the Magisterium with those who exercised it?  Magisterium, like the word "teaching" in English, can refer either to the ACT of teaching or to the things taught ... depending on whether you're considering the verbal noun subjectively or objectively.  But in no case does it mean the same thing as the teacher himself.

Then go ahead and give an instance, or an example of the magisterium being wrong - and another example of it not being so wrong as to lead people into heresy or reject the faith.

Go ahead.

  There's no theologian who would hold that the teaching of an Ecuмenical Council is not Magisterium.  

Just for clarity (not trying to stoke the fire), what do you guys consider the Second Vatican Council to be?

Just for clarity (not trying to stoke the fire), what do you guys consider the Second Vatican Council to be?

It was a council of the Church that should have never been convened. It was a robber council, a counterfeit council. It was the birth of the Novus Ordo church with new doctrines, new liturgy and new anti-Catholic religion, even had it's own Pentecost, The "New Pentecost".