These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Accidental Aesop: Hermione's subplot could be interpreted as, "Doing well in school is great, but your mental health comes first. If school is putting a strain on your well-being, it's not worth it."
Alternate Character Interpretation: Sir Cadogan, the portrait that takes over guarding Gryffindor Tower for The Fat Lady after she's attacked by Sirius Black, and whose work style involves setting "ridiculously complicated" passwords, and changing them at least twice a day. Is he stark raving mad, or Properly Paranoid taken Up to Eleven?
Ending Fatigue: Not too bad, but off to see Buckbeak get executed - diverted to shrieking shack, long Plot Dump, Werewolf ensues, time turner, going back though the evening and THEN it's over.
Fridge Brilliance: Snape asks Lupin if Harry might have gotten the Marauder's Map from one of the makers. Considering he went to school with the Marauders, and was likely insulted by them in the same way as the map (as well as familiar with their nicknames), he probably suspects that Lupin had something to do with the map - which he does.
In the film, the music Lupin plays during the Boggart lesson. Seems silly at first but then you realise he's trying to keep the mood light so the students will be able to imagine their worst fears as something comical.
The first time Ron and Harry notice Hermione has briefly stepped away from them between classes, she changes the subject by voicing her hope that there's something good for lunch, she's starving. Of course she's starving: she's just used the Time Turner to live through twice as many hours since breakfast as they did!
"Funny Aneurysm" Moment: At one point in Harry Potter and the Philosopher's Stone, Scabbers bit Goyle on the knuckle (which was even referenced by Fred and George Weasley in Azkaban). Come Azkaban, and the revelation that Scabbers was actually Peter Pettigrew, who was the true person responsible for leaking Lily and James Potter's location to Lord Voldemort and thus their deaths, not to mention the revelation in Goblet of Fire that Goyle's father was most likely one of Pettigrew's comrades among the Death Eaters it becomes somewhat disturbing.
Also Ron carrying him around in his pocket and Scabbers even fell asleep on Harry's bed at one point in Philosopher's stone.
Growing the Beard: Many fans believe that this is the turning point for the series as a whole, citing the encounter at the Shrieking Shack as evidence.
One-Scene Wonder: Aunt Marge only appears in one chapter, but still manages to be among the more despicable characters in the series, perhaps even more so than her brother Vernon.
Shipping Goggles: The series has enough of this to fill a page, but this entry probably has the best example, what has been dubbed "The Symbolic Flight". This theory states that because Harry and Hermione flew together on Buckbeak together and without Ron, that they are destined to be together - ignoring the fact that Ron was only not present because he broke his leg earlier.
YMMV tropes present in the film:
Accidental Innuendo: The scene from the book listed above is even more dodgy in the film, when Harry's Uncle Vernon keeps bursting into the room to find out what's going on. Vernon is played by Richard Griffiths, AKA Uncle Monty.
Big Lipped Alligator Moment: After everyone arrives at Hogwarts to start the new year, the Fat Lady won't let them into Gryffindor Tower because she's too busy trying to shatter a glass with her voice.
The talking shrunken head on the Knight Bus. But Rowling has stated that she finds the shrunken head hilarious and "wishes [she'd] thought of that."
Broken Base: Half the fanbase considers this one of the best (if not the best) Harry Potter film in the franchise, or at least when the Harry Potter films started getting good. The other half considers this movie to be one of the worst (if not the worst) Harry Potter film in the franchise. The film was mostly better received by critics than the first two, although it was the first HP film not to get four stars from Roger Ebert. Also, this is J.K. Rowling's favorite film.
Particular anger was given to Steve Kloves having his favorite character Hermione steal Ron's big moment of declaring Sirius will have to go through them to get to Harry, despite having a broken leg.
Growing the Beard: According to most professional critics, along with about half of the fans. At the very least, people agreed that the younger actors and actresses were finally fitting snugly into their roles (aside from the Narm mentioned below).
Internet Backdraft: Best movie in the series? Worst movie in the series? Middlingest movie in the series? Whatever your opinion, a huge chunk of the fandom will loathe you for it.
Narm: The movie is full of it, most notably Harry's crying scene in Hogsmeade (blame Daniel Radcliffe), Draco getting attacked by Buckbeak (blame Tom Felton), and the punching scene (blame Emma Watson, Tom Felton, andSteve Kloves).
Apparently "believing in yourself" equates to SHOUTING AT THE TOP OF YOUR LUNGS. No quiet confidence in the film version of the Potterverse. EXPECTO LOUDYELLUM!
Malfoy being attacked by Buckbeak, which was deliberatelyNarm-y; in the book, it was stated that he over-played how bad the injury really was. Why? Because he's Draco Malfoy and he's a whiny brat. And because he wanted to get Hagrid fired.
Sirius's "I Know You're in There Somewhere" Fight with Lupin, wherein he makes a futile attempt to use The Power of Love and The Power of Ham to convince Lupin to not turn into a werewolf. And then Lupin does turn into a werewolf, which looks like a balding chupacabra (unlike the book, where werewolves only have slight physical differences from normal wolves).
They Changed It, Now It Sucks: Alfonso's complete redesigning of Hogwarts geography, coupled with the overall more comedic tone the film has compared to the previous two.
Not to mention shrunken heads added to the Knight Bus.
The excision of the explanation of the identities of Moony, Wormtail, Padfoot, and Prongs, which confused many moviegoers who hadn't read the books. Especially since it would have been relatively simple to slip into Lupin's final scene.