I don't really know enough about Catholicism to have an in depth discussion, but I can say that I heard a coworker (in the United States) get into a heated discussion with another coworker about the pope's authority over him as a Catholic. Evidently, as far as he's concerned the pope has no authority over his religious beliefs whatsoever, which came as a surprise to me and pretty much everyone else present.
Admittedly, having grown up in a Protestant community, just about everything in Catholicism seems mysterious, but as an outsider I was under the impression that the Catholic church had a very strong notion of religious authority, where the pope could (in grossly oversimplified terms) say one day that women could be priests and that would be that. That's opposed to most Protestant denominations, where there's almost no central authority, and any individual church can always decide to just do things their own way if they don't care about leaving the conference they're part of (if they're even part of one).
Clearly, this is not a correct understanding of how Catholicism works.
Your coworker is probably exaggerating things to make a point, but he's largely correct (Disclaimer: I'm not a Catholic, I just read a lot about Christian religious history, and know some Catholics). The main power of the pope is that he's the head of a religious denomination and bureaucracy that over a billion people are members of. So what he says about religious matters is taken seriously, and he has some control over who gets appointed bishop and money matters. But the Catholic Church isn't and never was a one-man show, so there are plenty of people under the Pope who are also influential and counsel the pope and have their own jobs, like Vatican treasurer, or archbishop of Los Angeles, etc. So your coworker may or may not pay attention to what the pope is doing, but if he attends a church, his priest probably pays attention. And like Teneb and Grim Portent, said, Catholicism is not a monolith, and is very different in different places, because that's what happens with people.
There is a doctrine of Papal infallibility that says the Pope can make statements that are without error, or
ex cathedra. But those are pretty rare and there's limits over what this can be applied to. Wikipedia cites a list of 7 or so papal documents that are considered infallible, with the caveat that its not a comprehensive list. But the most recent of the 7 was from 1950. I think this is what Arcvasti is talking about.
I know pope Francis has been getting a lot of flack from conservative Catholics in the United States, some of whom are part of the Religious Right, because he's too liberal for them (mainly over the issue of divorced Catholics). I've also seen criticism of him for not doing more about reforming the papacy to prevent corruption and covering up sexual abuse, but I don't know enough about that to make a judgement on that.
Again, I'm also not a Catholic, so if any of this is wrong, feel free to correct me.