Continuity mistake: Before Father Karras walks into his mother's apartment the lights are on. In the next shot as he walks in the lights are off and he turns them on. (00:19:10)
Continuity mistake: Father Merrin watches three metal smiths working and the piece of metal on the anvil is red hot in one shot and not in the next. (00:05:45)
Continuity mistake: Father Karras says to Det. Kinderman, "It didn't happen in the fall?" And his right hand goes from holding the fence to being wrapped around the poll between shots. (01:05:30)
Continuity mistake: Father Merrin says, "Hear my prayer" as he puts his hand on Regan's head. If you look closely the vomit first comes out when her head is facing the right and it totally soils her blue nightgown. In the next shot with her head facing left there's nothing on her blue nightgown. (01:48:05)
Continuity mistake: When the full IV bottle falls and breaks during the exorcism, no liquid splashes out of it.
Continuity mistake: When Kinderman introduces himself to Karras at the track, he puts his ID in a pocket in his vest. The rest of the time they're talking and walking, he must be wearing a different vest because there's no pocket.
Continuity mistake: When Regan is in the hospital, to calm her down the doctor gives her an injection in the arm. In one shot her gown is up high on her shoulder, but in the next the gown is down around her upper arm - the doctor can hardly find room to inject her it's so low.
Continuity mistake: During the exorcism, the first time, the wardrobe door is cracked, but later it is solid.
Continuity mistake: The first time Father Merrin enters Regan's room, Chris is wearing a fur coat, because Regan's room is so cold, but when Damien closes the door, Chris's fur coat is gone.
Continuity mistake: Throughout the film it has been made clear that it's Autumn and it is cold. Leaves have fallen and they are crunchy on the ground. In the scene where Father Karras is walking with the detective they turn a corner and it's summer again. The sky in the scene goes from grey to blue and the trees have re-greened as they pass a tennis court with players in their short whites. (00:43:00)
Continuity mistake: As Father Karras listens to a tape recording of Regan at the university language lab we see the tape recorder running, a pen in his right hand and no ash tray or cigarette. In the next shot from behind smoke rises from a lit cigarette and the pen is on the desk. (01:29:15)
Continuity mistake: Damien plays the tape of Regan for the Language Lab Director and when we first see them a chair is in front of Damien. In the next shot the chair is gone and a coat appears next to him on his right. (01:35:30)
Continuity mistake: Damien starts the tape recorder in Regan's room twice between shots. (01:31:40)
Continuity mistake: As the Language Lab Director plays the tape of Regan backwards for Damien he turns on the wrong tape recorder. There's no indication that this is not the first time he's heard the tape and he uses the recorder on the left to listen, and is not dubbing anything onto the recorder on the right. When we hear the backwards tape he uses the recorder on the right which does not have the right tape spooled up and doesn't have an overdub of the original to play backwards either. (01:35:40)
Continuity mistake: Lots of stuff moves as Damien waits on the couch in Chris's living room as she pours him a drink. The flower pot on the back wall under the ceramic pumpkin moves to the left and the couch he's sitting on moves a couple of feet to the left. Later everything moves back. (01:34:00)
Continuity mistake: The Language Lab Director plays the tape of Regan backwards for Damien but if you look at the tape it's running in the same direction. (01:35:45)
Continuity mistake: Father Karras confronts Regan for the first time and just before she pukes on him fresh vomit appears on her night gown. Her eye makeup becomes darker and her hair is matted down also between shots. (01:25:35)
Continuity mistake: In the scene with the crucifix, Chris falls to the floor after Regan bashes her in the face. Look closely at the dresser that eventually comes sliding across the room at her. When we first see it, it's about half a foot to the right of the closet door on the left of the room, and is never touched or moved. When we see it again as it comes sliding across the room at Chris it's been moved to the left right up against the closet door. (01:19:10)
Continuity mistake: Chris first meets Damien on a bridge as two other people walk in front of him. In the next shot they're behind him. (01:19:40)
Continuity mistake: Det. Kinderman talks to Chris as they're having coffee in the kitchen and says, "My opinion, he was killed by a very powerful man" and her right hand appears by her face between shots. (01:14:20)
Answer: It was indeed Pazuzu, he wanted Regan to believe he was some friendly entity to gain her trust. Thus the Captain Howdy facade.