Continuity mistake: When the Dodo gives instructions to the lizard on how to rescue Alice he grabs his neck with the right hand. A shot later it's the left hand.
Continuity mistake: When giant Alice picks up the carrot and tells the rabbit she must eat something, her nails suddenly swap from normal to painted.
Continuity mistake: When being a giant inside the house, Alice extends her arms and they're quite short. A couple of shots later she remains the same size but her arms are now 5 times longer to allow for her to open the windows on the front. This has nothing to do with the magical cookies.
Continuity mistake: The first wide shot of giant Alice bursting the rabbit's house shows a barrel between her legs and a grandfather's clock leaning on her left ankle. Both disappear in the following shot.
Continuity mistake: Before the Dodo punches the lizard down the chimney and says "And drag it out", the visor on the lizard's cap is either facing backwards or frontwards between shots.
Continuity mistake: In the close-up of the oyster shells a salt shaker suddenly appears. There was no shaker previously; as a matter of fact, the carpenter said he was going to bring one but he never did.
Continuity mistake: The menu is printed in red and black colours. When the carpenter discovers the walrus has eaten all the oysters the menu is now printed in black and white.
Continuity mistake: When the carpenter asks the walrus if he wants some pepper the small menu on the table grows twice its size. Check the pattern of the tablecloth to make the math.
Continuity mistake: After the carpenter cuts the bread he tosses the saw up the air. Check the lower part of the table and you'll notice that the saw magically vanishes, it never continues its fall below the table.
Continuity mistake: The carpenter goes to the kitchen to fetch bread and pepper and leaves his plate on the table. When the Walrus leaves the menu standing the plate has vanished.
Continuity mistake: When the Walrus is about to eat the oysters and asks for bread, the carpenter's knife and fork disappear.
Continuity mistake: When the walrus leans the menu against a pot a spoon suddenly appears.
Factual error: The first shot of the calendar shows two days numbered as 20 and March ending on the 24th. In the following shot it's fixed.
Continuity mistake: The shell next to mother oyster's calendar is on the middle part of it, but a shot later it is on the left side of the calendar.
Continuity mistake: When Walrus walks inside the water to talk to the oysters, the calendar, plants and little blocks next to the mother oyster disappear in the wide angle only to reappear in the close-up.
Continuity mistake: After Tweedle Dee and Tweedle Dum do the Shake hands dance and say "that's manners!" the way Alice's skirt folds changes between shots.
Continuity mistake: During the Tweedle Dee and Tweedle Dum scene Alice walks inside a tree trunk. Its shape changes in every single shot at least 4 times.
Continuity mistake: While with the Dodo Alice sees the rabbit arriving ashore next to a stone. A shot later the stone disappears.
Continuity mistake: When Tweedle Dee and Tweedle Dum show up, the tree where Alice looks if the rabbit is hiding has a huge bush on the right that disappears a shot later.
Continuity mistake: When Alice arrives at the shore where the Dodo is her hair gets soaking wet when the waves crash on her, but the second time this happens her hair is dry and perfectly brushed and remains this way for the rest of the scene.
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