When King Azaz is first seen (in long shot) his costume has the purple and blue colors of the Mathemagician, instead of the correct colors of orange and red.
In the live action scenes Milo's eyes are blue, but in the animated world his eyes are brown.
When Faintly McCabre offers Milo and Tock some cookies, Tock eats all of them, yet in the next shot they are back.
King Azaz gives Milo a yellow bag, but when he pulls it out later it's purple.
When the Which says, "castle in the air" (and when Milo does after seeing it close up), there's no thunder and lightning.
During the live-action portion at the start of the film, as the kids run out of the school, the camera operator's shadow is briefly visible on the bottom right corner.
When Milo meets the Which, she addresses him by name even though he never told her what it was.
When they are traveling through the numbers mine, Milo says "Golly! And I used to think that numbers weren't important or valuable." The Mathemagician responds with " Not important! Not valuable! By the 4,827,659 hairs on my head, I'll tell you what's important! " The average head has between 100,000 and 150,000 hairs. Far below the amount the Mathemagician stated.
Character Azaz says, "mentioning numbers is against the law." He immediately proceeds to mention multiple numbers. Additionally, Officer Short Shrift, when arresting Milo and Tock, mentions the numbers.