(at around 17 mins) After Charlie goes crazy, he comes back with an oil can and sprays Big Bill in the face with the oil. We then catch a quick glimpse of Big Bill's back which is already stained black, but in the following long shot, his tank top back is pristine white in color.
After going on break, he turns both wrenches in the same direction. Before that he appears to be tightening them in opposite directions.
(at around 46 mins) When Charlie goes to let the gamin into the department store, the escalators are off, allowing him to rush down the stairs going up. However, when he goes back downstairs and notices the burglars, the escalator is working, allowing him to do his stunts.
(at around 33 mins) During the visit of the Minister in jail, Charlie sits next to the Minister's wife and they make funny noises. The distance between them varies between shots.
(at around 4 mins) When the wrench gets stuck on the bolt, Charles Chaplin loses hold of it, but he has it in his hand when the foreman comes by.
After the Gamin's sisters are taken away, there is no further mention of them or of the Gamin's concern (or lack of) for her sisters.
(at around 1h 11 mins) The juvenile authorities have a photograph of the Gamin included in their warrant, even though they never had the opportunity to take her picture, and there's no evidence of photographs in the humble home of the Gamin's family.
(at around 10 mins) When Charlie is in the Feeding Machine, a wire can be seen from the left, moving the rotating corn device.
(at around 15 mins) When Charlie comes back out of the machine, the footage is played backwards. The men hammering in the background give this away.
(at around 14 mins) One of the men on the moving line with Charlie, is operating a press/drill. When he moves it down towards the plates with the two nuts, it never actually touches the plates.
(at around 1h 14 mins) When Charlie tries to get the roasted duck dinner to the table, the items on his tray are fixed in place. The wine cradle barely moves when he swings the tray overhead, yet when the tray is on the table seconds later, it does.
(at around 52 mins) After Charlie has been doused with rum, his suit is soaked. When Big Bill recognizes him directly afterwards, his suit is mostly dry.
(at around 1h 17 mins) During the Singing Waiters musical number, the singers' lips do not match the soundtrack.
(at around 1h) During the scene with the press at the factory machine shop, Charles Chaplin leaves his boss's coat under the press, flattening his pocket watch. A trap door under the press is clearly visible as a stagehand accidentally leaves a corner of the coat caught in it, and Chaplin must yank on the coat twice to free it.
(at around 19 mins) The wire holding the flag on the back of the truck is clearly visible.
As the Gamin has work, the warrant for her arrest for vagrancy would be invalid.
Despite constantly showing no hesitation in stealing food and other items, neither of the main characters thinks to obtain a new set of clothes and shoes while in the department store. And this is not because of a lack of opportunity: for example, the girl wakes up and leaves the store (barefoot) at 6 a.m. before it opens at 9:30.