Continuity mistake: In the scene where the Scarecrow comes down off the pole and onto the yellow brick road, some of his stuffing falls out. You can then see Dorothy pick it up and put it back in. After Dorothy agrees to take the Scarecrow with her and they begin to skip away, you can see the straw that Dorothy supposedly picked up and put back inside the Scarecrow on the road again.
Plot hole: In the scene where the Wicked Witch is furious because Dorothy and pals have been saved from the poppy field, the Flying Monkey hands her a golden cap. She then dashes the cap across the room. The golden cap is used in the book to summon the Flying Monkeys. They shot scenes involving use of the cap, edited them out, but left this one with the cap inexplicably being tossed about.
Continuity mistake: When Dorothy comes running into the farm at the beginning of the movie, there's a lone cow in the pen behind her and a couple of white chickens that she ends up chasing in the direction of the camera as she runs near the house. Two shots later the cow disappears and the white chickens are now in the pen.