Visible crew/equipment: Near the beginning of the movie, the old priest is in Northern Iraq and you can see the shadow of a microphone on his hat.
Continuity mistake: When Chris is taking a walk with the priest Damien, she throws her cigarette to the ground, but in the next shot it's back in her hand again.
Revealing mistake: Crash mats are visible on the steps, when the Father is thrown through the window and rolls down the stairs.
Deliberate mistake: Father Merrin says, "It is He who commands you", and we hear and see the ceiling crack above his head. In the next shot we see the ceiling above him and they are no cracks in it, but four shots later we see the exact same spot and now cracks appear even though we hear no more cracking over-dubs after the first one. (01:49:15)
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: As the first part of the exorcism comes to a close, Father Karras picks the blanket up off the floor and covers Regan with it. Father Merrin's red prayer book can be seen on the left night table but in the next shot it's moved and we see his crucifix there instead. (01:53:00)