Other mistake: In the ceiling tea party, Mary Poppins offers Bert some sugar, and when he responds that he would not like any, his Cockney accent is gone.
Other mistake: As Admiral Boom's assistant is loading the cannon a third time, he puts the red rocket in nose first rather than stick first.
Other mistake: When Admiral Boom orders the gun to fire on "the Hottentots" (the sweeps) the rockets sticking out are in the order of a small red on top, a large green in the middle, and a large red on the bottom. A moment later, he orders another salvo, but the rockets are in the same arrangement. The chances of the arrangement being identical twice, unless done carefully, are very slim.
Other mistake: After Bert and the others dancing on a railing that should have moved, as it did when they jumped off, three sweeps walk back and forth on their hands over the street between buildings. After dropping to only their toes to hold them up, you see them drop all the way down, then stand, where there was no surface in sight to do that on.
Chosen answer: They recorded her singing in two separate parts and fixed them together. The editors did a good job on it! It may have been made a long time ago but even then the technology was quite advanced enough to carry out that scene.