(at 40 minutes into the film) The doctor is killed in his car. When Lenore looks at the car, its bloody broken window is different when viewed from both the outside of the car and the inside of it.
When in the operating room, the vital signs monitor displays "DEMO".
When the sheriff is driving the patrol car, you can see the shifter is in Park and the ignition is in the Off position.
It took the police over a day to check Dr. Baldwin's office and when they radioed back, the cop was on the same stretch of road in front of the same mountain.
Near the end of the film, the power goes out in the Davis house, yet the doorbell works when the cop rings it.
Cops need a warrant to search a house and to get a warrant they need probable cause, so the female cop asking Sgt. Perkins if she needed to call for backup before they knew if anyone was home and before they heard any yelling makes no sense.