Visible crew/equipment: When Peter first arrives at Neverland we see Smee taking Captain Hook's hook to the ship. When the camera pans underneath the ship's sails to reveal the giant human skeleton attached to the prow you can see a metal walkway at the top of the screen, behind the sails, and the legs of some crew members stood on it. (00:37:23)
Visible crew/equipment: When Peter first arrives at the Lost Boys hideout, as he stands up (and the shot moves backwards), you can see the cameras shadow on the ground on the far left side of the screen. (00:49:29)
Continuity mistake: During the school play, at the beginning of the movie, Peter's phone rings and Moira stops smiling and turns to face him twice as he answers it. (00:02:06)
Continuity mistake: At the beginning of the school play Moira turns to Peter and says "Watch your daughter, she's stealing the show" and you can see two fathers stood behind Peter filming the play. The shot then changes to a wider angle of the audience and these two men have suddenly stopped filming and their cameras are nowhere to be seen. (00:01:14)
Continuity mistake: When Pockets is shooting paint at the pirates, he sprays yellow paint on a pirate's face on the right, who crouches and touches his face blinded. Shot changes and not only is the painting gone, but the pirate is calmly sword fighting with a kid. (01:53:38)
Continuity mistake: When Peter recalls himself alone in the rain with a teddy bear by his side, the bear is sitting upright in the first shot, but resting against the baby with its head skewed in the following angle.
Continuity mistake: Peter is lying in the cradle with Tinkerbell flying around, the fluttering of her wings making his hair messy. When he stands up his hair is neatly brushed to the right.
Continuity mistake: After Jack removes his Hook-styled wig his hair is messy and caked. Then the fight starts and the next time we see him his hair is shorter, cleaner and perfectly brushed.
Continuity mistake: During the insult war the black kid next to Peter leans forward and fakes a puke. When the shot changes he's sitting still.
Continuity mistake: The green haired mermaid is very close to Peter, but a shot later she is far away, swimming towards him.
Continuity mistake: In the plane, the way the note book is held changes between shots: by the top or by its side.
Continuity mistake: When a lost boy fires balls at the pirates, they slip and fall on the deck. Angle cuts back to the boy firing and the deck is suddenly spotless and empty, and the same pirates repeat the previous actions.
Continuity mistake: When Pan is about to kill Hook and his daughter grabs his arm and says "Please daddy, let's go home", Pan's arm swaps from bent to straight between shots.
Character mistake: When Hook has Pan under control, the kids start to say "I believe in you" in turns. The second one, a red haired boy, can't help staring at the camera.
Revealing mistake: When Peter sees Tink in a night dress, the shots from behind reveal an obvious doll. Note how it does not have any fluffy hair (or any hair at all) as opposed to Tink's.
Continuity mistake: When Hook and Peter's battle starts, Hook's sword falls on the floor. Its position changes between shots.
Continuity mistake: Before the crocodile is about to fall on Hook, he is either lying on a shadowy place or a sunny one, depending on the shot, no continuity at all.
Continuity mistake: After Hook trips over the clock, the position of the kids in the background increases/decreases randomly between shots.
Continuity mistake: After the clock falls on the ground and Hook trips over it, he ends up kneeled, head sunk, and starts to remove his cape. When the angle changes he is now lying down, face up, and removing the cape again.
Revealing mistake: During the pirate ship scene where Peter's kids are lifted in the net, the sea in the background is a blatant backdrop with a very obvious blue painting with zero detail.
Answer: 1) Though it is never fully explained, the mystical way Peter Pan would come and go from Never land. 2) It was Smee who was doing the spying. When Hook asked Smee, "This can't be my great and worthy foe?" Smee replied, "I have all the information here." He had a file of paper work on Peter. 3) Hook knew where the Lost Boys were, When Peter asked, what happened to the Never Tree. Tinkerbell said, "Hook burned it when you didn't come back." He considered the Lost Boys not worth the effort. It was Peter, he wanted.