Continuity mistake: The police station that they stop at is in a very out of the way rural community with only a few people in the jail. However, once the demon enters the jail and the alarm is sounded there are at least 20 cops on duty - all at the station in the middle of the night, in the middle of nowhere.
Continuity mistake: There are at least two different 1960 Chevys used in this film. There is a noticeable difference in the front bumpers. Notice the front bumper area just below the headlights. The first car used has a plain straight bumper, the second one has little chrome trim riser mounted just below the center of the headlights. The second one first shows up at the cat lady's house. The lower tag pan also changes.
Continuity mistake: When the main characters visit the house of the old woman with the cats, she comes out and aims at the monster with a double-barrelled shotgun, and fires one shot. Then when she goes back into the house, two shots can be heard in quick succession. She must have re-loaded the empty barrel quickly...
Continuity mistake: When the Creeper bumps their car at the early stages of the film, the boy turns his head to the left to see the back. Then suddenly the camera angle shifts and we see him turn his head to the right this time to see the back, which of course he couldn't have done that quickly.