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Other mistake: At Skull Rock, when Peter Pan mimics Captain Hook's voice while talking to Smee, just as he says, "Oh, and one more thing," note the handle of Peter's dagger. The animation of his dagger is bizarre, the handle's grip is separated from its pommel, as if it's going through Peter's forearm. (00:41:50)
Answer: In the original stage play by J.M. Barrie, he was a bank clerk. I don't think what he did for work was brought up in the 1953 film.
Bishop73