http://www.newadvent.org/cathen/07790a.htm
(... cut and paste answer to a cut and paste charge)
OBJECTIONS ALLEGED
The only noteworthy objections against papal infallibility, as distinct from the infallibility of the Church at large, are based on certain historical instances in which it is alleged that certain popes in the ex cathedra exercise of their office have actually taught heresy and condemned as heretical what has afterwards turned out to be true. The chief instances usually appealed to are those of Popes Liberius, Honorius, and Vigilius in the early centuries, and the Galileo affair at the beginning of the seventeenth century.
Pope Liberius. Liberius, it is alleged, subscribed an Arian or Semi-Arian creed drawn up by the Council of Sirmium and anathematized St. Athanasius, the great champion of Nicaea, as a heretic. But even if this were an accurate statement of historical fact, it is a very inadequate statement. The all-important circumstance should be added that the pope so acted under pressure of a very cruel coercion, which at once deprives his action of any claim to be considered ex cathedra, and that he himself, as soon as he had recovered his liberty, made amends for the moral weakness he had been guilty of. This is a quite satisfactory answer to the objection, but it ought to be added that there is no evidence whatever that Liberius ever anathematized St. Athanasius expressly as a heretic, and that it remains a moot point which of three or four Sirmian creeds he subscribed, two of which contained no positive assertion of heretical doctrine and were defective merely for the negative reason that they failed to insist on the full definition of Nicaea.
Pope Honorius. The charge against Pope Honorius is a double one: that, when appealed to in the Monothelite controversy, he actually taught the Monothelite heresy in his two letters to Sergius; and that he was condemned as a heretic by the Sixth Ecumenical Council, the decrees of which were approved by Leo II. But in the first place it is quite clear from the tone and terms of these letters that, so far from intending to give any final, or ex cathedra, decision on the doctrinal question at issue, Honorius merely tried to allay the rising bitterness of the controversy by securing silence. In the next place, taking the letters as they stand, the very most that can be clearly and incontrovertibly deduced from them is, that Honorius was not a profound or acute theologian, and that he allowed himself to be confused and misled by the wily Sergius as to what the issue really was and too readily accepted the latter's misrepresentation of his opponents' position, to the effect that the assertion of two wills in Christ meant two contrary or discordant wills. Finally, in reference to the condemnation of Honorius as a heretic, it is to be remembered that there is no ecumenical sentence affirming the fact either that Honorius's letters to Sergius contain heresy, or that they were intended to define the question with which they deal. The sentence passed by the fathers of the council has ecumenical value only in so far as it was approved by Leo II; but, in approving the condemnation of Honorius, his successor adds the very important qualification that he is condemned, not for the doctrinal reason that he taught heresy, but on the moral ground that he was wanting in the vigilance expected from him in his Apostolic office and thereby allowed a heresy to make headway which he should have crushed in its beginnings.
Pope Vigilius. There is still less reason for trying to found an objection to papal infallibility on the wavering conduct of Pope Vigilius in connection with the controversy of the Three Chapters; and it is all the more needless to delay upon this instance as most modern opponents of the papal claims no longer appeal to it.