Deliberate mistake: After Captain Hook pushes away the boat, Mr. Smee loses the oars, and in the next shot, the oars are back.
Continuity mistake: When Wendy reminds Peter about Tiger Lily, as he rescues her from the water Tiger Lily is wearing low brown moccasins, but as they're flying out of the cave at Skull Rock, she's wearing green boots. Also, Peter's sheathed dagger is now at his left. (00:45:35)
Continuity mistake: At Skull Rock, after Captain Hook skewers his own feathered hat, when Peter draws his dagger the sheath promptly vanishes from his right hip and shortly reappears. Then it vanishes again, and reappears when Peter calls Hook a codfish on a hook. (00:43:10)
Continuity mistake: While Tiger Lily is being held at Skull Rock by Captain Hook, her dress has red and lavender stripes around the neckline, with the lavender closer to her neck. When Smee is rowing the boat, the two colors near Tiger Lily's neckline have switched in this shot, with the red now closer to her neck. (00:39:30 - 00:41:05)
Continuity mistake: In the first few shots on the Jolly Roger, the pirate with red long hair has a wooden leg on his right side, which then switches to his left side. This switch continues in later shots. (00:20:45)
Continuity mistake: After Peter Pan saves Wendy, the dagger sheath switches sides. (01:05:07)
Continuity mistake: During a sword fight between Peter Pan and Captain Hook, the dagger is in Peter's hand and when he flies towards the rope ladder, the dagger is suddenly back in its sheath. (01:06:57)
Continuity mistake: After Peter cuts the rope around the mast where the kids are tied, there's a brief shot of Peter standing sideways on the mast. Look below and you'll notice that the ropes have vanished.
Continuity mistake: The first time we see the pirates a group of them are doing dagger-throwing at a chalk drawing, but in the very first shot the drawing is missing.
Deliberate mistake: During the first aerial angle of the pirate ship they are heard singing, but the ship is empty. Most surely due to the complexity of drawing detailed tiny pirates.
Continuity mistake: Wen Michael warns John and the lost boys about the Native Americans he is kicked out. In the aerial angle Michael's teddy bear disappears.
Continuity mistake: When the pirates attack the crow's nest where the kids are, one of them cuts his moustache with his sword. Later on his moustache grows back.
Continuity mistake: When we see the windows of the Darling nursery, at the start and at the end, their height repeatedly switches between having either five or six horizontal rows of glass panes.
Audio problem: After the mermaids splash Wendy, she raises a seashell threateningly above her head and says "If you dare come near me again.". Her mouth doesn't move at all.
Continuity mistake: In the scene where the crocodile attacks Hook at Skull Rock, there is a shot where the croc bites Hook's left foot and the shoe comes off, leaving Hook's left foot bare. In the shot with Hook wrapped around the croc's snout, the shoe is back on Hook's left foot and his right foot is bare. (00:44:50)
Continuity mistake: During the bomb present scene, Peter Pan's dagger is missing.
Continuity mistake: Before Michael is abducted by the Native Americans his pajamas swap from pink to white.
Continuity mistake: During the final fight, the sail is supported with two ropes and a pulley. Next shot, the sail is only supported with one rope and no pulley.
Continuity mistake: During the final fight, the Jolly Roger flag disappears and then reappears.
Continuity mistake: When Peter is setting sail to London, the empty dagger sheath has disappeared.
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