Revealing mistakes: When Scrooge is lighting the lamp to perform a search of the house, it is obvious that the lamp is an electric light.
Continuity: When Bob Cratchit closes the place where he and Scrooge work at the beginning of the film, he locks the door with a key, however at the end of the film when Scrooge walks around town singing, he goes to the place where he and Bob Cratchit work opening the door without a key.