Continuity mistake: 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 mistake: 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 mistake: 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 mistake: During the Lion's song of, "If I only had the nerve." You can see the cameraman's shadow pass over Dorothy, the Lion, and then the log on the side of the road. Watch carefully, it comes back.
Revealing mistake: When everyone is still in the poppy field, after the snowstorm, Dorothy says "Look. Emerald City is closer and prettier than ever." Look behind the Lion just as Dorothy says the word "City" and you'll see that the wire attached to his tail brushes over the top of some of the poppies, knocking the snow off.