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: Neverland very much runs on "If you believe, it will happen" which is what Tink means during the meal when she says "If you don't imagine yourself as Peter Pan you won't be Peter Pan." So by the rules of Neverland, as soon as Peter believed it was real it was then real. The dinner was trying to teach him to believe as, in Neverland, if you don't believe it then it won't happen.