Continuity mistake: When Carlotta brings the plates for the meal they all have a dome cover with a top handle, but when Sebastian runs across the table those handles have changed. (00:54:50)
Plot hole: They go and buy Anne Marie a whole new wardrobe. So, how come in the remainder of the movie she continues to wear her old rags?
Continuity mistake: The snowman hits his nose with a hammer, completely bending it in half. In the next shot it is suddenly magically straight again.
Continuity mistake: Gromit uses the handbrake to let the ship take off, but when travelling between the Earth and the Moon there is a shot of the control console and the handbrake has disappeared.