Continuity mistake: When they first meet the Tin Man, the Scarecrow is holding an apple in each hand. He drops the one in his right hand but the other one disappears when he reaches for the oil can. Later when they all walk away both apples, and the one that Dorothy dropped before, are gone.
Continuity mistake: In the beginning of the movie Dorothy comes running into the farm and there's an old tire hanging from a tree. Two shots later as she walks away from Aunt Em and Uncle Henry the tire has been moved. The angle at which it hangs has been changed and the piece of rope hanging on the bottom of it is now three or four inches closer to dead center than it was before.