Revealing mistake: Crash mats are visible on the steps, when the Father is thrown through the window and rolls down the stairs.
Revealing mistake: As Father Merrin speaks to another archaeologist in the beginning of the movie the clock on the wall stops between ticks and he turns around to look at it. It's easy to see that the clock pendulum has been pushed up against the window from behind in order to make it stop. (00:06:45)
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.