I do not believe the Pope apologized, but even if he did, it does not nullify his infallibility.
The Bible itself gives a clear example of how the Bible works.
But when Cephas came to Antioch, I opposed him to his face, because he stood condemned. 12 For prior to the coming of certain men from James, he used to eat with the Gentiles; but when they came, he began to withdraw and hold himself aloof, fearing the party of the circumcision. 13 The rest of the Jews joined him in hypocrisy, with the result that even Barnabas was carried away by their hypocrisy. 14 But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas in the presence of all, "If you, being a Jew, live like the Gentiles and not like the Jews, how is it that you compel the Gentiles to live like Jews?
Galations 2:11 - 14
Both Catholics and Protestants agree that Peter was infallble. Catholics believe he infallible because he was the first pope. Protestants believe he was infallible because he was an apostle. No matter. Both see this passage as being problematic. How can Peter be infallible while being rebuked for doing something wrong?
As a Protestant, I never heard an explanation that satisfied me. Only when I became a Catholic did it all make sense. It fits with the Catholic Church's teaching that the Pope is only infallible when he speaks ex cathredra.
Peter was not speaking officially, in fact, he did not speak at all. He withdrew from the Gentiles. Paul was not critical of his teachings but his action. Paul condemn for not living up to his own teaching. Infallibilty only relates to the official teaching. Peter was wrong in his actions, but still infallible.
In the same way, Pope Benedict could apologize for an action he did, or for saying something unofficially that is wrong.
But still saying this, the Pope had noting to apologize about. His classroom lecture was about intolerance. He quoted from an emperor in the Middle Ages about how evile the Muslims were. He was endorsing the quote from the emperor. He was using the quote from the emperor as an example if intolerance.
But that being said, I do believe that the Pope made a mistake. In fact, two. He underestimated the media and he underestimated Islam. He mistakenly thought that he could quote from someone he obviously disagrees with, without being taken out of context. He did not realize that the media is ready to pounce on any sentence that could be take out of context. He did not realize that there are many Muslims who
want to take something the Pope says out of context as a pretext for more violence. He needs to be more careful, realizing that there are enemies ready to pounce on anything he says. But this does not effect his infallibiity, this just means he is a little naive about how the real world operates.