Continuity mistake: In the plane, the way the note book is held changes between shots: by the top or by its side.
Sacha
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.
Sacha 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.
Sacha 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.
Sacha 
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.
Sacha Continuity mistake: When Hook and Peter's battle starts, Hook's sword falls on the floor. Its position changes between shots.
Sacha 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.
Sacha Continuity mistake: After Hook trips over the clock, the position of the kids in the background increases/decreases randomly between shots.
Sacha 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.
Sacha 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.
Sacha Continuity mistake: When Peter is grabbing the mast trying to touch his kids' fingers, in the wide angle half of his body is stretching out towards them. A frame later, from another angle he is in a different position, totally crouched.
Sacha Continuity mistake: When Smee introduces Hook, his brass speaker swaps hands between shots.
Sacha Continuity mistake: While Wendy shows Peter her Peter Pan book, one can see the tip of her right finger holding the page, but a shot later from a wide angle, her right hand is nowhere to be seen.
Sacha Continuity mistake: After Wendy tells Peter about Neverland, the bronze elephant sculpture on the night table swaps from facing left to facing forward between angles.
Sacha Continuity mistake: When Wendy tells Peter about Neverland, his fringe swaps from falling over his eyebrow to perfectly brushed by his forehead, between angles.
Sacha Continuity mistake: After the kids have been abducted, Wendy tells Peter about Neverland. The pillows behind her swap from wrinkled to perfect between shots.
Sacha Continuity mistake: In London, Liza grabs Jack by his scarf and drags him violently inside. When the angle changes, she is hugging him softly.
Sacha Continuity mistake: In the plane, Peter's daughter shows a drawing with the plane burning. Depending on the angle she's either crouched next to the paper or standing away from the paper. This swaps back and forth.
Sacha Revealing mistake: Set lighting screens are reflected on the office guy who's recording the baseball game.
Sacha Continuity mistake: During the opening school play, the girl with Peter Pan is standing tall. When the angle changes she is suddenly kneeling down.
Sacha 
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.