In the song "Painting the Roses Red", after Alice sings "Oh, pardon me, but Mister Three, why must you paint them red?" the three cards say "Huh? Ohhhhhhh!". When they say that, The three of clubs card has a three in the bottom right corner with no clubs symbol on top of the three. the three of clubs also has nothing in the top left corner. The ace and two of clubs have nothing in both of their corners. A few slides later, the symbols in the corners come back. (Possibly a chameleon-ability similar to the Caterpillar.)
During "The Walrus and the Carpenter", the appearance of the walrus' eyes is inconsistent between shots. Some shots have just little black dot eyes, while some shots have him with full pupils and colored eyes.
Just before the flowers sing "All in the Golden Afternoon", we see an orange dandelion tuning up. Between him are two other dandelions, one purple one on the left, and one red one on the right. Two shots later, when the scat-singing begins, the two dandelions have switched places.
The Caterpillar's colors are reversed when he says "Keep your temper." Normally, his body is blue-violet and his belly is light blue, but for that shot the body is light blue and the belly is blue-violet. Many creatures of reality as well as fantasy have color changing abilities.
During the tea party, the "half a cup" changes its configuration, and the seating arrangement changes when the March Hare is smacked with a hammer. Although probably not intentional, these goofs fit in with the absurd, disorienting humor of the scene.
When the Caterpillar changes, he loses his arms and legs. During the chase scene at the end of the movie, when Alice swims up to him on his floating mushroom, his arms and legs are back. This is part of his biology.
At the start of the film, Alice is sitting on a tree branch as her sister Lorina sits at the base of the tree reading aloud, but when Alice wakes up at the end of the film, she is sitting in Lorina's spot and Lorina is standing up. It is possible that Alice fidgeted and moved around significantly while in "Wonderland", and Lorina changed her own position accordingly.
Towards the end of the scene with the flowers, the flowers are asking Alice what kind of flower she is. There's a shot from above, looking down on Alice. Behind her, we see her shadow on the ground. Although Alice is moving a bit, the shadow is perfectly still.