Continuity mistake: When Dorothy first meets the scarecrow, there is a patch of grass in front of the field the scarecrow is in. On the grass there's two beds of flowers. The flowers change colors from when Dorothy meets the Scarecrow, to when the Scarecrow starts his "If only I had a Brain" song.
Continuity mistake: At the witch's castle, the witch throws a sand timer to the floor from a banister, and it smashes in front of a large group of her guards. But in the next shot, when the candle chandelier lands on all the guards, you can see that the smashed timer has disappeared.
Continuity mistake: In one of the most endearing scenes from one of the greatest movies of all times, nobody noticed that as Dorothy sings "Over the Rainbow" the haystack she's standing next to just materializes between shots. Later it disappears long before the twister reaches the house. If you watch the movie you'll see the exact spot where the haystack should be seen as Aunt Em gives Dorothy a cruller and says to her, " and find yourself a place where you won't get into any trouble".