When the man in a "coma" is strapped to the chair; and he is shown at a full body shot, the strap around his neck only covers his neck and does not cover his chin. When he is shown with a close up of his head, the strap covers is neck and his chin.
(at around 1h 4 mins) When Bug rips out all the tubes and leads connected to the sleeper as he backs out of the door the EEG leads are still connected to the sleepers head. In the next shot, when Jay looks back at the sleeper, the leads have been disconnected. In the next shot of the sleeper where he stirs to indicate he's not dead, you get a shot of the EEG recorder showing brainwave activity yet the shots of the sleeper show that there are no EEG leads connected to him.
(at around 42 mins) While Jay re-tells the story of the Demon to Holly, when the camera pans out from the top of the special tank, you can see that it's empty and the door is closed instead of open when Holly comes in.
(at around 1h 5 mins) When the group leaves the cell the sleeper is being kept in, the image on the surveillance monitors shows the sleeper's head in a different position from when the group left him just a few moments before. Also, the brace around his neck is closed although Bug left it open.
(at around 3 mins) The opening credits show "Bitterroot Mountains, Montana". The Bitterroots are actually located in Idaho.
When telling the story about the Sleeper, it was said and shown that he had bitten his tongue when he was a child. At the end of the movie he is speaking without any problems, which is impossible without a tongue. The same things happens with Peter, who also bit off his tongue when he was possessed by the Sleeper. Later in the movie, when he is lying on the floor, dying, he speaks normally.