Revealing mistake: When the coconut flies at Peter, there are a couple of flashes of light reflected from the device used to connect wire to the coconut.
Revealing mistake: As Peter pulls himself up to look over the brick wall, the entire snow drift on top moves, showing it's set dressing.
Revealing mistake: As Tink flies around waking up the Lost Boys, as she flies by the red-headed kid, the wires operating the puppet are visible.
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.