During the song "Spoon Full of Sugar", Mary Poppins walks over to a window and picks up a bird. If you look carefully, you can see the wire that the anamatronic bird is attached to.
No slip up here, it was such a big deal that they used animatronics in this movie it was advertised at the time, with that scene as an example. However, obviously they weren't going to be as good forty years ago as they are today, sometimes you cannot fault movies because they didn't have the technology to hide stuff.