The tournament arc was torture and in retrospect I have no idea why I watched it at all. I only watched up to the end of the 4th season and didn't read the manga. I may be speaking for myself, but I never liked BNHA and it is worse than many other shonen series.
Most of the characters looked odd and lacked cohesion. The world felt overly simplistic, even by shonen standards. Western comic book superheroes are uninteresting to me and whatever influence that had on the series leaves a bad taste in my mouth. All Might manages to be slightly less gay than Superman, so I'll give the author that.
Thematically, giving Deku one of the most powerful quirks within the first few episodes was ridiculous and undercuts any messaging throughout the show. What does Deku really prove by trying to become the strongest hero when his power was basically handed to him? We're told that he is supposedly analytical and intelligent, but I don't see how that is reflected in his character at all. It's more like he injures himself to add fake tension and "effort" with almost no strategy. He's more retarded than Naruto, which is really saying something.
More of a personal issue with the series, but I also wish there was more of a focus on romance or deep friendships between characters.