Factual error: In the scene where Arthur first enters the house and starts going through paperwork, there's a shot of Nathaniel Drablow's death certificate which shows 'body was not recovered' in the box next to his cause of death. Such a thing would not be written on death certificates of the time - that box is reserved for 'Signature, description and residence of informant', a heading which can partially be seen as the camera pans across the certificate. For the death to have been registered, an informant's signature would have to have been there.
Visible crew/equipment: About an hour in Arthur walks outside after answering the knocking, you can see in the reflection of the window to the left, a light simulating the lightning.
Factual error: The driver who first takes Daniel Radcliffe to the haunted house tells him that the tide will be out at 5pm, enabling him to return and collect Radcliffe. A day or two later, Ciaran Hinds says it will happen at 11pm. This is not possible - tide times cannot change by that much in the space of a couple of days.
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.
Revealing mistake: When Mr Kipps comes back in into the house after seeing the ghosts of the children in the front garden, he looks down and sees footprints. The error is the footprints are far too uniform and equally spaced at regular intervals to look natural. It looks as though a template has been used to print them on the floor.
Revealing mistake: When Arthur goes into the marsh to bring Nathaniel's corpse up, each time he emerges to get air, you can see the lack of mud around his lips from an air mask.