Angst Dissonance: At various points in the story, most recently chapter 20, it's established that someone snapping their fingers can trigger Peter's PTSD, but for some readers, it's hard to get invested in that aspect of his character when it's so inconsistent, what with there being numerous instances where Peter sees or hears someone snap their fingers-even doing it himself, on occasion-and he has no reaction. Further reducing the drama around it is that it doesn't inspire sympathy, it inspires confusion- Peter was not there to witness Thanos' Snap. He was on another planet, and just started to randomly disintegrate.
Izuku automatically wins his fight with Iida because the latter had to leave to see his brother in the hospital after he was attacked by Stain. While it's a logical reason, Ingenium was attacked in the semifinals in canon, but he ends up attacked in the first round here, and there isn't a lot to suggest that the Sports Festival had been dragging on longer than it did in canon. (Can be argued that the tiebreaker fight between Parker and Iida, as well as the Bakugo-vs.-Pony match being possibly longer than the canon first few rounds, made it drag a bit longer, but it's still pretty flimsy.)
In this story's version of the Hosu Incident, All for One is somehow able to give Shigaraki fifteen Noumus-over twice the amount that was available in canon. Nothing had been done to imply that Noumu production had been going better than it was in canon, so it feels like it was thrown in simply to make for bigger action. Later reveals in the manga (Kurogiri's status as the Super Prototype Nomu and the Doctor's Power Copying technology) have lessened this to a degree, but mainly retroactively.
Many readers felt Bakugo crossed the Moral Event Horizon when he unknowingly insults the Avengers (who Peter thinks are dead). Others think the MHA!Civilians would agree with him.
To a further extent, Bakugo's characterization as a whole is this. In general, the story portrays him as being a far bigger asshole than he was even in the beginning of canon; to some, it's justified by the story being told primarily from Peter's point of view, thus having Bakugo be colored by a somewhat Unreliable Narrator, but to others, it comes off as little more than Bakugo being hit with the Ron the Death Eater trope. For what it's worth, one of the authors has stated that they have nothing against Bakugo.
Mirko. While some think that Is she is a Pragmatic Hero who gives various good points despite her rather abrasive delivery, stating the various holes in Peter's technique, others find that many of her accusations are unfounded due to being unfamiliar with Peter's situation. Not helping matters is her rather villainous move of nearly injuring Peter because she can't control her temper and openly admitting she only cared about his safety because it might hurt her career.
The Sports Festival has created a lot of this, mostly with the fighting portion:
Shinso, one of the biggest Ensemble Darkhorses of the fandom, gets taken out with ease by Sato, of all people. For some, it's justified in-universe by Sato already knowing about Shinso's Quirk and from how, from a meta-perspective, he already managed to be in the spotlight a bit during the War of the Flags, but for others, the quick loss just does a disservice to his character, an opinion further enforced by one of the writers outright saying that they don't like him. Still, there are those who feel that Sato gets virtually no character development while Shinso is massively overhyped, so there are multiple points of view on it.
Peter and Mei's fight made one for playing out the same as Mei's fight with Iida. Many people hated that Peter ended up embarrassing himself on national television for largely avoidable reasons, but others didn't have a problem with it and saw it as harmless fun. For what it's worth, it's not like it would be the first time Spider-Man made a fool of himself in public.
Bakugo and Pony's fight, specifically the fact that Bakugo won through excessive violence. Some people object to it because they feel that Bakugo didn't deserve to win if he needed to be so brutal to make it happen, but others are fine with it since it was a fair fight and Bakugo ends up seeing Pony as a Worthy Opponent, plus it's mostly Peter who sees the win as Bakugo going too far. A third camp, however, hates that Bakugo won simply because they hate Bakugo.
Peter’s constant praise and the plot revolving almost entirely around his actions is another point of contention. Some believe that Peter’s string of wins and focus detracts from his character as an underdog, while others enjoy seeing his wins against characters like Bakugou for the Catharsis Factor. Most readers think that a story about Peter as a student of UA isn't a bad idea, but the constant praise and how overpowered Peter feels make it less than enjoyable to read.
Eraser Head, and later Mirko, dropping bricks on Peter's Fighting Clown attitude and wishing he'd be more serious. Some readers agree, while others argue that the two of them are being idiotic for failing to realize that it's a (typically effective) weapon Peter uses to make his enemies more angry and less focused, while also trying to keep an optimistic mindset (similar to how All Might always strives to keep smiling no matter what). Compounding the problem is that Eraser Head gets his wish when Peter defeats (and nearly kills) Bakugou during the Sports Festival, so he knows just how scary Peter can be when he's completely serious, and yet he still wants Peter to drop the snark (obviously without having it replaced with kill-crazy).
The Hero Killer Arc. The choice of Mirko as Peter's mentor has been met with a lot of negative reactions due to her not teaching Peter anything, her violent behavior, and that for many reviewers her actions painted her as, at best, a hypocrite and at worst a psychopath who cares more about fame than being a hero. However Peter was also in the wrong for not being able to trust the heroes who were already on the case such as Endeavor and Edgeshot to take care of Stain. Also Mirko was greatly concerned about Peter's Death Seeker tendencies and what it could lead to which Peter later admitted to.
Creator's Pet: Some have accused Peter of becoming this. Mostly due to the entirety of the fic being focused on him, the characters' lives revolving around his actions, winning a majority of his battles, laying a curb stomp on Bakugou, and almost every girl seeming to find him inexplicably attractive. This isn't isolated to just the readership's thoughts, as even the story's co-authors have called Zaru out on being heavily favoring towards him.
Fourth Wall Myopia: In short, a lot of the Broken Base surrounding Peter's relationships with the likes of Eraser Head, Mirko, and Bakugo stems from this trope.
A lot of the reason for Peter and Bakugo's conflict being so divisive is due to this trope. Peter sees Bakugo as little more than a selfish jerk, but the audience knows that he's had Hidden Depths from day one; Bakugo sees Peter as little more than a showboating goof, but the audience knows that he's gone through – and is still going through – his own Trauma Conga Line, so the fact that the characters keep fighting because of their shared lack of fourth-wall knowledge results in fans going back and forth on who's in the right.
The recent incident of Bakugo accidentally insulting the Avengers ended being a huge example of this; while many people were quick to label it as Bakugo crossing the Moral Event Horizon, that only works because the readers are the only ones who would be aware that Bakugo said anything wrong.
Peter constantly missing Tony was bad already, but it gets even worse now that we know he dies in Avengers: Endgame.
Peter ending up in a world where no one knows who he is seems bad enough, but considering how his original fate was that no one in his home universe would remember Peter Parker after the events of Spider-Man: No Way Home makes things all the more painful. The fact that he lost everything in both scenarios makes things even worse.
Launcher of a Thousand Ships: As Spider-Man often is, Peter has been shipped with nearly every girl he's interacted with.
Too Cool to Live: The Iron Spider suit was basically a major Story-Breaker Power that put Peter far ahead of his classmates than he already was. The Stark nano-tech combined with Peter's natural abilities alongside the armor's unique features made it pure awesome. In the fight against the USJ Nomu, it gets completely wrecked with no way to repair it. Co-author IKnowNothing confirmed that the armor is not returning at all due to both the aforementioned story-breaking aspect alongside no one (not even Peter) knowing how to repair it. Though LD has stated that while he's not against the idea of it returning, that will only happen when Peter starts facing competition that he can never reasonably best with his own abilities or creativity.
they hate Bakugo.