Continuity mistake: During the "Why Should I Worry" song, Dodger goes with his "scarf" of sausages through a basin full of wet cement. Logically the cement should be stuck on the sausages, though that does not appear to happen, even though the sausages went through the cement. There is cement on his paws, though, that he needs to wash off.
Continuity mistake: As the movie begins, on the sidewalk in front of a store there is a box filled with kittens and a sign reading "Kitties - need home." The words "need home" are in all capital letters. In the close-up, only the "N" is capitalized and the rest of the words are in small letters.
Continuity mistake: As Jenny and Winston first enter the front door of their 5th Avenue flat, notice how the right-hand window significantly changes its distance in relation to the door when seen from an exterior versus interior perspective. Initially the window is one space away, but this soon changes to two spaces when Winston removes his hat and coat in the following shot.