The Sherman Brothers (Robert B. Sherman and Richard M. Sherman) came up with the idea of Mrs. Banks being involved in the suffragette cause to explain why she should be so neglectful of her children.
The old woman in the park Bert talks to in the beginning of the film (with the two tall daughters) is Mrs. Corry. In the book she ran the sweet shop in the park and in the Broadway show this is where they buy the letters to make the word "supercalifragilisticexpialidocious". The shop is mentioned once by Mary Poppins in the film before she and the children make a detour to Uncle Albert's house.
When the constable brings the children home after Katie Nanna quits, Michael tries explaining why they ran off. While he is saying, "It was windy out," you can clearly see Jane mouthing that very line while he is saying it.
When Mrs. Banks bends to embrace the children (when the Constable brings the children back from the park), her head is turned to her left rather than looking at her children, obviously anticipating Mr. Banks' line which cuts off her embrace.