Deliberate mistake: After Captain Hook pushes away the boat, Mr. Smee loses the oars, and in the next shot, the oars are back.
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.
Deliberate mistake: When the kids are in the crow's nest fighting the pirates, dozens of stones and arrows fly out of nowhere, despite the kids just having a handful. Check for the kid with the blowpipe: He manages to blow dozens of rocks out of nowhere. There's even a shot where arrows and stones are flying from all over the place despite the fact that a shot later the kids are crouching.
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