It survived as long as it has because it was able (at times) to be a big tent and encompass such a variety of people and points of view. Yes, there was the inquisition but honestly if they were ALWAYS burning people who disagreed with the party line, there would be nothing left.
I suppose this "saint and sinner" persona is no different than any other church or even each Christian but perhaps because of it is so old, it is so big, it so visible you notice it more.
Kristof says in his piece:
So when you read about the scandals, remember that the Vatican is not the same as the Catholic Church. Ordinary lepers, prostitutes and slum-dwellers may never see a cardinal, but they daily encounter a truly noble Catholic Church in the form of priests, nuns and lay workers toiling to make a difference.
I believe this is true of not just the Catholic Church, but as the church catholic as well.