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.
YMMV: Peter Pan
Mainly from the novel or play
Adaptation Displacement: It's often forgotten that it began life as a play, before being adapted into a novel (both by JM Barrie).
And it's often forgotten that while the play was Peter Pan's first incarnation a a story, the character of Peter Pan goes back further still, to his debut in Barrie's novel The Little White Bird.
In everyone who goes to Neverland; in Peter himself so much it's scary.
The one thing he ever briefly has angst over is the fact that he had no parents, and he'll never have a family or know true love because he can't grow up, which is a bit of a Tear Jerker. In Hook he gives in to this and leaves Neverland.
Toy Ship: Peter and Wendy. Also Wendy and Hook, depending on the handling of the adaptation.
Unfortunate Implications: J.M. Barrie's depiction of the Native Americans is just awkward. For a start, "Piccaninny" isn't an actual tribe, but an old slur to describe black children. "Squaw," which isn't even a real Native American word, has a history of being used in a derogatory manner toward NA women in a manner similar to a particularly offensive English word. And then there's that whole Honor Before Reason thing.
As with everything else in Neverland, the Indians are never intended to be realistic, but rather they are typical 19th century British children's concept of Indians. Neverland has childishly stereotypical Indians for the same reason it has childishly stereotypical pirates, because they're natural inhabitants for a British children's dreamscape of that era. Doing research to make them realistic would have been Completely Missing the Point. Not that any of this necessarily makes it any less awkward for modern readers, of course.
The Woobie: Say it with Wendy and me, everyone—"Poor Tootles!" Despite being the only Lost Boy who might accurately be called "nice", he's Born Unlucky and his self-esteem is virtually non-existant. Not to mention that he's always saying things like this:
"I did it...When ladies used to come to me in dreams, I said, 'Pretty mother, pretty mother.' But when at last she really came, I shot her."
Adaptation Displacement: The movie adds "star" to the book's quote "Second star to the right and straight on til morning", which is almost invariably how the phrase is quoted, often even with mistaken attribution to Barrie.
Disney has done what it can short of censoring the film. For instance, the Blu-Ray has a feature that allows the viewer to jump to each of the film's musical numbers, but "What Made the Red Man Red" is not one of the selections available.
Ho Yay: Hook and Smee. Smee seems to live for nothing more than serving Hook, which he does quite cheerfully. He's also quite the bumbler, and yet Hook hasn't killed him yet, despite shooting a man for singing distractingly or hurling one overboard for an irksome comment. He also calls exclusively for Smee with insane gusto any time he needs saving, and during the 'life of a pirate' song there's the affectionate little feather tickle Hook gives Smee, and Smee seems quite smitten by it. In Return to Neverland the octopus gives Hook a kiss with one sucker, which Hook accepts with no problem because he thinks it's from Smee. Smee also gives the Captain a rough massage.
Tear Jerker: Tinkerbell's death in the sequel. Jane hearing that it'll happen soon and rushing back towards the tree, calling out for her. She arrives too late and finds Tinkerbell dead. Although she is revived two minutes later, it's still quite the heart-wrenching scene - especially with the reprise of "I'll Try" playing over it.
Unfortunate Implications: The racism in J.M. Barrie's book is awkward enough today, but Disney takes it Up to Eleven. One of the most glaring examples are the juxtaposition of teepees and totem poles - these belonged to two completely different cultures, and are as awkward and unrealistic as the Eiffel Tower in Moscow. The song What Made the Red Man Red? also implies that the "red man" used to be white (Eurocentricism/Anglocentrism).
The Indians obviously aren't meant to represent any specific tribe or culture (in fact at the time the novel was written "Indian" was used to mean almost any low-tech native culture). The fact that so many stereotypes in the scene are played to negative and comical effect have quite enough Unfortunate Implications on their own.
Return to Neverland portrays Jane as unreasonable that she worried about the things around her, such as whether her soldier father will die in World War II and the freaking London Blitz.
Values Dissonance: Watching "What Made the Red Man Red?" today can be uncomfortable to say the least.
Hilarious in Hindsight: All the talk about Peter being afraid of love and of his own sexuality becomes funny if you know that Jeremy Sumpter went on to star in a notoriously bad Lifetime movie about a teenager getting addicted to internet porn.
Jerkass Woobie: Peter. Hook too, to some extent, but this version constantly squanders this sympathy.
Nightmare Fuel: The more monstrous portrayal of the mermaids and the only one to date to actually show the stump of Hook's severed arm.
Hook's eyes actually do turn red as he attempts to murder an unarmed Peter Pan.