The gaslights used in the movie are all naked flames. By the 1930s, gaslights used mantles, which gave off a lot more light for less gas and didn't smoke the glass covers. Also, gaslights were largely controlled by clockwork (still used in historic areas today in London and other European cities), so the leeries' main job would have been maintenance: mantle replacement and winding the clockwork rather than daily lighting/dousing.
In the London street scenes, several of the buses shown are too old for the 1930s setting. For instance, the buses are shown with outside staircases to the upper deck, whereas those designs (from post-WWI) had been superseded by then by designs with enclosed staircases.
When the children are going to the shop and don't have enough money, they mention buying things at 'half-off'. This is an American phrase that would not be used by a child in London who would say 'half price'.
Tuppence invested for 20-some years would be more likely to result in bus fare than pay off the mortgage on a house. As such, some viewers have speculated that Mr. Dawes Jr.'s story about that investment is an excuse for the bank president to arbitrarily forgive Michael Banks' debt in view of his nephew's treatment of him without it appearing to be an act of charity.
When Mary Poppins lands with the kite, she is holding the kite back-to-front, with the struts facing forward. If one has ever made, or flown a kite, one will know that this impossible - a kite cannot fly like this.
When Cousin Topsy performs a handstand during her dancing routine, her earrings do not dangle down to the ground. This shows the scene was filmed with her putting her hands on a surface above her head and subsequently being rotated 180 degrees in post-production.