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.
Revealing mistake: If you listen closely, during the singing of "We're Off To See The Wizard" by Dorothy, the Scarecrow and the Tin Man, you can recognise Buddy Ebsen's gravelly voice. He was the original Tin Man, but had a reaction to the makeup. They had already recorded the songs and it was too expensive to re-do it. (This film was WAY over budget and they couldn't waste time and money re-recording songs)
Other mistake: When entering the Haunted Forest, the Scarecrow is carrying a pistol and a stick, the Lion has a bug sprayer and net, the Tin Man has a monkey wrench and his axe. But different scenes after that shows some items missing and then returning. I guess in the insect scene that was cut, they lost all those things but the axe.
Continuity mistake: When Dorothy is at the end of the movie confronting the Wizard about going home, since she killed the Witch, Toto goes over to the curtain and you can see him tied up to it as he opens it. Dorothy then goes over there and automatically has him in her arms - she didn't even need to bend down and pick Toto up.