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.
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. (00:12:20)