Continuity mistake: When Arthur and the dog are returning from the graveyard, the dog stops to sniff at something and Arthur walks ahead a couple of steps, leaving the dog behind him. The shot changes and the dog is now in front of Arthur.
Continuity mistake: Daniel Radcliffe's facial hair goes from 2 day stubble to clean shaven throughout the movie. About midway through it is very noticeable. He is by himself in the Marsh house, for the 2nd time I believe, and in every shot he has 2 day stubble. However when it cuts to a close-up he has a near-perfect shave.