Continuity mistake: The father tears the children's advert for a nanny up into 8 pieces, but when it comes out of the chimney it's in far more bits.
Continuity mistake: At the bank where the elder Mr. Dawes appears from the back room, he makes it as far as the edge of the step in that shot. In the next shot, he's back by the door walking again to the edge of the step.
Continuity mistake: At the end of the film, Mary Poppins flies away from the Banks's house (supposedly within a short distance of the City of London), however, she is then shown flying towards the City on a route that would take her over the Banks's house on the way, had she not already flown over it.
Continuity mistake: During the first few scenes, you see Jane is missing a tooth but the tooth disappears and reappears throughout the film.
Continuity mistake: When Mr. Banks takes the children to the bank, and they meet the directors, first the children are standing close together, with Mr. Banks right behind them. Later, when the elder Mr. Doors is talking to them, Mr. Banks is next to Michael and the children are farther apart. Later still, when we see Michael close up, Jane is out of the shot altogether, meaning that she is even farther away from him than previously.