Visible crew/equipment: When Professor Higgins is having Eliza practice saying the letter H by blowing into a tube to make the flame waver, the paper she's holding is actually Rex Harrison's lines. Once the paper starts to burn and the camera angle changes, you can read them and it's practically all of his lines for the whole scene.
Visible crew/equipment: As Mary Poppins walks over to put the hat stand in place, the shadow of the camera plays on her dress.