Revealing mistake: In the scene with the three chimneys, the sweep coming out of the middle chimney can be seen actually coming up from behind it, as his arms going up are visible.
Revealing mistake: After Bert pulls up his pants to bring the dance challenge to an end, as he walks to the other side of the clearing, both he and the background can be seen through the penguins.
Revealing mistake: As Mary and Bert sit at the Penguins' tea tent, when Bert calls for the waiter, the background shows through his head, revealing the live action matted in over the animation.
Revealing mistake: As the turtle closest to the camera struggles with Bert's weight, Mary's heel clips through the turtle's beak. Also, though a combination of animation and live action, neither Bert or Mary has any kind of reflection on the water, real or otherwise.
Revealing mistake: When Mary Poppins goes to bring out the hat stand and the mirror, you can tell that the underside of the table is masked with a overlap of the background to make the illusion complete. Also, when she pulls out the mirror, watch the table leg closest to her, and the bottom of the mirror pass, because the illusion is not quite far enough to cover it.
Revealing mistake: After Michael and Jane have been sucked into the chimney and then pop out, Mary Poppins pops out a short time afterward. When she does so, a dark, obvious cable can be seen supporting her.
Revealing mistake: Near the end of the movie after Mr. Banks throws the kite in the air and the camera shows the kite, you can see a white wire to the left of the kite that isn't the kite's string that pulls the kite over.
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.