The first time the mother puts the electrodes on the son his shirt is wide open on his chest from the above angle. Then during the switch to the side angle his shirt appears much less open, and then back to the above shot with it opened wide.
The path to the lake on a stormy night looks freshly shoveled.
Dr. Wilson calls the police while driving to Mary's (the protagonist) home. Even though it shown to have taken him several hours to get there, the police are not only nowhere in sight, they haven't even been to her house. Despite this, the doctor doesn't attempt to call them again.
When Mary and Tom are on the boat dock, despite the weather being well below freezing, you can't see their breath.
In the last scene of the movie, the mother is speaking to the little boy who is in the right side of the back seat, presumably so she/we can see him and his drawing clearly. When they get out of the car he exits through the left side door. Not an error, but unusual that he wouldn't get out on the right...they are making the shot easier.
A child is declared missing after somehow finding his way to his former psychologist's home during freezing, winter weather. Not only aren't police overly concerned about the matter, when local news reports are shown, this is somehow not the major story.
Doug is found dead outside the home with no explanation whatsoever, as he had already asked her earlier that day if she needed anything before he left. At that time, the son was in the chair, and the mother was in his room, so he wouldn't have had time to kill him on the way out.