Continuity mistake: When the king says he needs witnesses to judge Alice, the pile of books changes position in every shot.
Continuity mistake: When the Cheshire cat reappears to show the way to the Queen's castle the branch on the right keeps changing style in almost every shot. It doesn't have to do with fantasy, dreams or anything plot-wise.
Continuity mistake: The handwriting on the "Don't step" sign changes between shots, specially the apostrophe on the first sign.
Continuity mistake: When Alice sees the first sign of the sentence "Don't step on the mome raths", it has 3 nails, one on the middle upper part and two on the middle lower part. A shot later there are just two nails on each opposite side of the upper part.
Continuity mistake: When Alice leaves the Hatter and Hare the wide shot of them toasting not only does it not show all the mess they've made, but it is the exact very first shot we saw of them when Alice arrived.
Continuity mistake: When the Mad Hatter squeezes a lemon on the clock, jam is spread all over the machinery. A shot later there's just a small pile of jam.
Continuity mistake: When the Mad Hatter pours jam in the clock the mess on the table disappears. Also, all along that scene the objects around are not continuous between shots.
Continuity mistake: When the Mad Hatter smashes the clock its distance to the teapot next to it increases between the first and second shot.
Continuity mistake: When Hatter and Hare cry "move down" the spoon, the yellow cup and saucer in front of Alice disappear.
Continuity mistake: When the Mad Hatter shouts "Pick up" Alice is given a yellow cup. The white and pink cup in front of her suddenly disappears between shots.
Continuity mistake: While scolding Alice the Mad Hatter puts his elbow inside a cup. The colour and shape of the cup changes between shots.
Continuity mistake: When Alice tells the Hare "I don't quite understand" the spoon next to her appears and disappears randomly between shots.
Continuity mistake: When the hare tells Alice it's very rude to show up uninvited the pink teapot to her right disappears and the spoon swaps from straight to bent.
Continuity mistake: When the Unbirthday song ends a white cup and saucer appear next to the Hatter.
Continuity mistake: When the Mad Hatter says "oh me! he grabs the pink cup but a shot later he's got the yellow one and the pink cup is back in the hare's hand.
Continuity mistake: The amount of teapots and dishes on the tables increases and decreases randomly when the Mad Hatter and the Hare of March toast.
Continuity mistake: The colour and position of the teapots on the Mad Hatter's table is an absolute chaos: First they're pink, yellow and white, then in the close-up green and blue teapots appear. When Alice stands by the head of the table the colours change again and they stop moving despite the music still sounding.
Continuity mistake: When Alice leaves the Cheshire cat the trees are missing many of the signs that were there in the beginning.
Continuity mistake: The Cheshire cat says "of course he's mad too" while standing on the middle part of a very long branch. Shot swaps to a front angle and the branch is shorter and he is really close to the tree trunk.
Continuity mistake: When Alice is in the forest from the aerial angle the eggs are white, later on they become violet.
Chosen answer: There is no real answer. It is intended to be left unknown. See http://www.straightdope.com/classics/a5_266.html for The Straight Dope's answer.
Guy