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.
Acceptable Targets: Jack describing Peter's work as a lawyer causes Wendy to reply "Peter, you've become a pirate!" Later, when Peter tells the Lost Boys he's a lawyer, not a pirate, they still don't have any qualms about killing him and he says, "I'm not that kind of lawyer!" (Note that to them adult = pirate; they don't actually know what lawyers are but figure it must be bad too since he's an adult.) Even Peter himself tells a couple of lawyer-jokes at a dinner party; "There are some things even rats won't do."
Peter: You know, I remember you being a lot bigger.
Hook: To a ten year old, I'm huge.
Alternative Character Interpretation: Peter at the beginning is already dedicated to his family, he just gets overwhelmed by his many commitments. Moira's treatment of him is basically emotional abuse.
Angst? What Angst?: Peter and the Lost Boys are more sad about their good-bye than the fact that Rufio was killed a few minutes ago!
This was a major point of the original story; anyone who died was instantly forgotten.
Big Lipped Alligator Moment: The scene in which Tinkerbell suddenly, temporarily grows to human size to remind Peter why he's in Neverland. It's even been admitted by the filmmakers to be only there because Julia Roberts wanted to act directly alongside Robin Williams for once.
Colbert Bump: The film was already fairly well-known, but it gained even more recognition and popularity after a.) Homestuck made a Running Gag out of the film and the character of Rufio and b.) the Nostalgia Critic reviewed it.
Maggie's song "When You're Alone" was also nominated for an Oscar.
While this is not actually part of the movie, this musical remix of the movie definitely counts.
Detractor Nickname: Julia Roberts actually had one amongst the crew because of how she treated everyone: "Tinkerhell".
Ear Worm: The pirates chanting "Hook! Hook! Where's the Hook?!"
Ending Fatigue: There are several false starts to the Peter-Hook battle, and after that's wrapped up, as Roger Ebert put it, "Then comes the ending of the movie. Or the endings. One after another. Farewells. Poignancy. Lessons to be learned. Speeches to be made. Lost marbles to be rediscovered. Tears to be shed." And now you know why this movie is 2 hours and 24 minutes long (which, at the time, was seen as excessive for a family-oriented film).
Even the film's detractors tend to praise Bob Hoskins' Smee.
Foe Yay: Towards the end, Hook asks However did you manage to fit into those smashing tights again, Peter?.
Fridge Brilliance: In most performances of Peter Pan, the actor who plays the children's father also plays Captain Hook. In this story, the children's father is Peter Pan.
This isn't taking into account that not only did Wendy call Peter a pirate in the first act, but Hook then went and developed a father/son relationship with Peter's son Jack for a good chunk of the second and third acts.
A bit of brilliance that is mentioned elsewhere on This Very Wiki is the fact that when Tinkerbell first appears onscreen, she's speaking English, whereas in every other version of Peter Pan she "speaks" with a chiming noise, because only people from Neverland can understand her. However, the only person she speaks to outside of Neverland is Peter. That's the clue; for everything else Peter has forgotten about Neverland, he can still talk to faeries.
"Funny Aneurysm" Moment: Peter's family flies to London on Pan Am... which went out of business a week before the film premiered. Pan Am would've still been on its last legs when the film was under production, so it counts. (Spielberg declared he didn't want to remove it as the sole reason for the brand inclusion was the Visual Pun regarding "Pan")
Hilarious in Hindsight: Glenn Close has a cameo as a male pirate (the one that gets thrown in the "Boo Box" just before Peter first confronts Hook). Cut to 2011, when Close plays a woman masquerading as a male butler in Albert Nobbs, a role that got her nominated for a Best Actress Oscar.
Hollywood Pudgy: Peter keeps getting described as fat by the Neverland denizens (save for Thudbutt, who's the Big Fun of the Lost Boys) when he first arrives. He magically sheds a lot of it for the fight.
Well how else was he going to fit into those smashing tights again?
Neverland runs on imagination. It you believe the Training Montage is effective hard enough, it becomes true.
Ho Yay: Bob Hoskins said that he portrayed Smee's character as though he was in a homosexual relationship with Hook.