Continuity mistake: In the beginning while Dorothy is still on the farm, she walks along the pig pen fence and then falls in. When Bert Lahr picks her up out of there her dress is perfectly clean. (00:03:45)
Continuity mistake: During the Blue Birds in the Moonlight song you can see Gulliver holding his drink. In the next shot while he's laughing the drink has disappeared.
Continuity mistake: When Casper the Caveman takes off his caveman's outfit to go swimming, he puts his outfit near the edge of the bank. After Daffy says that he can't swim, he reverses back onto the land and goes and collects his suit, but this time the suit is now much further away from the bank.
Continuity mistake: When Juliet comes onto to the balcony during the performance of Romeo and Juliet, the moon is initially on the left of the painting behind her, but in the next shot it is now next to the balcony.