In the scene where Sullivan is in bed with a cold the girl sits next to him on the bed, she shifts between being at higher level with him and then same level as him from shot to shot. (This happens more than once in same scene.)
When Sullivan and The Girl enter the giant communal sleeping room with the other tramps, the sign on the wall behind them mentions writing a letter to your mother. The sign is still there when the cook comes to wake them up, but in wide shots, the sign moves further left and a different sign is in its place.
When the supposedly unconscious Sullivan is being pulled by a bum who hit him into an empty boxcar, you can see the actor (Joel McRae) push himself along with his foot, apparently because the other man is not strong enough to drag him.
When Sullivan is outside the boxcar door, encouraging the girl to jump out to him, the background scenery is unsynchronized. From the live-action shot taken outside, he is trotting along safely at about five miles per hour, but seen from inside, the scenery is moving behind him at breakneck speed, giving the illusion that Sullivan is being dragged on roller skates.