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: When Scarecrow, Tin Man, and the Cowardly Lion are marching into the Wicked Witch's castle after taking the guards' uniforms, all three of them are shown holding the same types of spears as the guards, so when they go rescue Dorothy out of the locked room and Tin Man chops through the door with his axe, where did the axe come from?
Continuity mistake: As the chandelier falls on the guards at the witch's castle, all the candles are blown out by the time it lands. The next shot shows some of them relit.
Continuity mistake: Immediately after Dorothy throws the water onto the witch, there is a long shot of the group as they observe the Wicked Witch beginning to melt. In this shot you can see that the Scarecrow's arm is still on fire, yet nothing is done about it as they all focus on the Witch. In the next full shot of the Scarecrow the fire is completely out.
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.
Character mistake: While singing the "If I Were King" song, the Lion asks, "What makes the Sphinx the Seventh Wonder?" The Sphinx is not one of the Seven Wonders of the World; its neighbour the Great Pyramid of Giza is. Besides, how would the residents of Oz know about our Seven Wonders of the World?