The difference, of course, is that their churches don't claim that their leaders have it within them to be infallible.
I don't really know the answer to the following question: Is it possible for a Pope to be removed at all? for malfeasance?
The Eastern Orthodox absolutely claim that an ecumenical council, once "accepted" by the church, teaches infallibly.
You, yourself, believe that the Apostles taught (at least when they wrote Scripture) under inspiration. Inspiration is a higher charism than infallibility, so yes, you absolutely claim that the leaders of the church in the apostolic era were infallible under some circumstances, in fact that they were more than infallible.
That's a question of interesting theological debate among Catholics. What would happen if the Pope proclaimed blatant heresy; if tomorrow, the Pope stood up and said, "Jesus did not bodily rise from the dead"? Some would argue that such a statement would be discernable as heresy, and, thus, the supposed Pope would be demonstrably an anti-pope. Indeed, some believe that John XXIII and Paul VI were anti-popes because they could not reconcile those pope's attitudes towards Protestantism with those of Trent. Such are called "sedevacantists."
I believe that's an easy way out, a theological cheap shot by those who are unconvinced that the Pope never would proclaim heresy. One of the apologisms for Catholicism is that the true church must be visible. Here, it must be noted that Alexander VI's most notorious, well-document sins (such as the paternity of his son) were before his elevation to the papacy. I can imagine that some pope could be found, by reason of grave sin, to have abandoned the faith, but such an occurrence would need to be spectacularly evident. Absent such a visible sign of apostasy, I would have to argue that the question, "what would happen if a pope proclaimed heresy?", is like the question, "what would happen if a triangle became square." It cannot be.