[Campion]

I'm trying to figure out how an infallible Pope can apologize for something a previous Pope did, and still claim that Popes are infallible.

You are very confused.

"Infallible" means "capable of teaching without error," not "incapable of sin or wrongdoing." The Pope goes to confession weekly; he is a sinner, as we all are, and admits it.

The 4th Crusade's attack on Constantinople was not "something [the] Pope did". It was something Catholics did, however. It's a historical fact that the Pope at the time condemned the acts of the Crusaders in sacking Constantinople.

[FactQuest]

That is a significant difference from the "normal" meaning of the word. I could, by the same rules, say that I am "perfect," as long as I explain that by "perfect" I mean that in my heart I try to be perfect.

That aside, working with the novel definition, what about Vatican II?

[Revenge of Sith]

That's right. Innocent III excommunicated the Crusaders who sacked Constantinople because they disobeyed his orders to attack the Holy Land.