Continuity mistake: One of the tiles comes loose when Wallace is walking across the ceiling in the museum. A few seconds later, the tile is flat against the wall again.
Continuity mistake: The hatch the mechanical arm comes out of doesn't appear on the helmet until Wallace is actually inside the building, and it also disappears later.
Audio problem: When Gromit is knocking on his bedroom door to get Feathers McGraw to turn the loud music off, his bangs are out of sync with the sound produced.
Continuity mistake: After Gromit runs away he starts looking at signs. In one shot, a blue sign goes over the one Gromit is reading (Room to Let), but in the next shot it's not.
Continuity mistake: In the beginning Gromit is pouring tea and there is a teacup and toaster near the pot. Gromit sets it down, gets the mail, and then comes back. When he comes back, the cup is much further away from the teapot and the toaster is on the other side of the table. No one has been in the room since Gromit left.