Continuity mistake: After the exorcism, Regan's wrists are tied together, but are then later seen tied to the bed.
Continuity mistake: As they talk, Det. Kinderman describes how Burke Dennings was found, "with his head turned completely around, facing backwards". In the next shot they're standing in a different place. At first Father Karras has a shiny fence clamp on the right of his head than in the next shot it disappears. (01:05:20)
Continuity mistake: After Chris puts her to sleep and walks down the steps, Willi the maid is cleaning up Regan's mess on the living room carpet from the previous party scene. We saw a nice close-up of the wet carpet as it happened and now Willi is not even close to cleaning the right spot. In fact she's kneeling right on it, yikes. (00:44:20)