Deliberate mistake: Det. Kinderman walks up the stairs where Burke Dennings fell to his death and looks up at Regan's window. This could not possibly be the outside of her window because when we see the room from the inside as Chris closes the window near the beginning of the movie, there's at least 6 to 8 feet between the window and corner of the house. Now when we see it as he looks up, the window is right at the corner of the house. (01:12:35)
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)
Revealing mistake: You can see wires in the scene where Regan levitates above her bed in the exorcism scene, lifting her up. The way they pull on her dress is also visible.
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)