Revealing mistake: In the shot of Tinkerbell flying across the screen with the vine (to trip up the Lost Boy twins) if you look closely you can see the wire that is attached to the vine, which is being used to pull it across. (00:52:50)
Revealing mistake: When Captain Hook reveals the blackboard with the "lesson" written on it, he underlines the word 'Hate' with chalk. However you can clearly see a faint smudged line already under the word (from a previous take) exactly where Hook draws the line. (01:05:45)
Revealing mistake: After arriving in Neverland in the bedsheet parachute made by Tinkerbell, there is a shot of Peter poking his finger up through the bedsheet to make a hole for him to rip open. However you can clearly see a small pre-made tear in the sheet for where he could easily poke his finger through and rip a hole in the fabric. (00:34:25)
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.