Continuity mistake: When Mary Poppins starts to read the "qualifications", the paper she reads from is whole, with no kind of indication that it had ever been torn. After a quick cut to George and back to the paper, the closeup of the paper reveals the lines where it was torn. Also in this scene, when she comes in, she has white gloves on. In the closeup on the paper, the gloves are gray, and a few shots later, they're white again.
Continuity mistake: When Mary Poppins is reading the childrens' torn-up note to Mr. Banks, she is wearing a pair of white gloves. The next shot is a close-up and she is wearing black gloves. And then finally a room shot, where she's wearing white gloves again.