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.
Factual error: The Robin that comes along in the movie is an American Robin, not a British Robin.
Revealing mistake: When all four actors are up on the rooftops, look closely at them when they all step onto the smoke platform that brings them down. All four actors are doubles. (01:46:50)
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.
Revealing mistake: An early scene with the constable and the children, Jane silently mouths along with one of Michael's lines.
Revealing mistake: In the scene where Mary Poppins is removing the large plant from her carpet bag, Michael inspects the underside of the table, where the table leg casts a shadow across his face. When Mary crosses in front of him (still under the table) she does NOT cast a shadow, although she should.
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.
Revealing mistake: In the tea party on the ceiling sequence, 2 shots after Uncle Albert tells his long underwear joke, Jane does a backflip in the air. If you look closely you can see the imprints that wires that she was hanging from made on her dress. (01:15:55)