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the buses are shown with 'outside' staircases to the upper deck, whereas those designs (from post-WWI) had been superseded by then by designs with enclosed staircases.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 Mary Poppins lands with the kite, she is holding the kite back-to-front, with the struts facing forward. If you have ever made, or flown a kite, you 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.