Continuity mistake: Buster Keaton drops his coat on the sidewalk in front of a light post. When he returns for it in the next shot, the coat has moved and wrapped itself around the pole.
Continuity mistake: After the Tramp has found the Kid as a baby, he sits down by a drain and contemplates dropping the baby in. He puts his cane alongside him, so that it is at right-angles to the pavement (pointing towards the camera). The shot changes, and suddenly it is now parallel with the pavement.