I'm Not Sure if the Pope Is the Legitimate Pope

There is a period in the church's history that was called the pornocracy because of how pornographic century popes were. But even if it wasn't, they aren't making some statement on faith and morals in an infallible kind of way. Popes make mistakes. They sin. They commit errors from time to time. None of that contradicts what the church teaches about papal infallibility. All of that is within the scope of what we believe is catholics. Trying to hold the papacy to this impossibly high standard explains why jesus permits a bad thing to happen, it's just that's bad theology.