Can't make mistake?
I generally like the movie. It does strike me as a very "60's" movie: clearly, the makers thought it would be relatively easy for the Catholic Church to turn into a liberal institution. If you just had several cardinals who favored liberation theology, the direction of the church could be changed.
There is one theological point in the story that I suspect is a little off. Towards the end, when he's perplexed by what to do, Pope Kiril says something like, "one consolation is that I can't make a mistake." I don't think that's really the Catholic doctrine. The church doesn't deny that popes can make mistakes. It sets forth a pretty narrow definition of what is infallible about popes.
Actually, I think the idea of papal infallibility is close to meaningless. One person I knew who is quite knowledgeable about theology said papal pronouncements about artificial birth control and other things are not necessarily infallible. So what is? One Catholic "answer column" I saw in the 80's admitted there is uncertainty about just what is infallible. One of the few recognized infallible doctrines seems to be papal infallibility!
I think saying the pope is infallible amounts to no more than saying you're willing to respect his authority. But others might say the same while holding fundamentally different understandings of what he teaches.
"Extremism in the pursuit of moderation is no vice."