Deliberate "mistake": There are two actresses playing Dorothy (and two dogs playing Toto) as she opens the door to Oz. The first is a stand-in wearing a dull colored dress in order to make it look black and white. After she opens the door and moves out of the way, Judy Garland is who we actually see walking through. Look at the different pleats on the two dresses.

Continuity: During the sequence where Dorothy meets the Scarecrow, Dorothy's pigtails are first short (above her shoulders) and as the song progresses her hair gets longer (below her shoulders), then short, and then long again.

Revealing: During the scene when Dorothy and Scarecrow are fighting with the trees, Scarecrow says "I'll show you how to get apples" and he gets hit by the apples. The very next scene if you quickly look at Dorothy's shoes, you can see that she is wearing black shoes, not her ruby slippers.

Revealing: When the guard tells Dorothy that she may not see the Wizard, Dorothy starts crying and tells a sob story about Auntie Em. Then, it shows the guard crying, but the tears aren't coming from his eyes. They're coming from above his eyebrows.

Visible crew/equipment: When the Lion is pulling up the Tin Man with his tail on the way to the castle, you can see a square block inside the Lion's costume to hold the tail on.

Continuity: When trying to escape the Witch's castle, the big doors close, and the gang stand in a line and start banging on the doors. Between shots Dorothy and the Tin-man switch sides.

Continuity: When the Witch melts, the broom is laying several inches from her dress. In the next shot, the broom is practically touching her dress.