Continuity mistake: Chris says to Carl, "We've got rats in the attic" and he replies, "Rats?". All the items on the table to her left have been rearranged between shots as she turns towards him. (00:12:40)
Continuity mistake: As they speak about Regan, Chris sits down at his desk and a shadow appears on Dr. Klein's forehead that wasn't there in the previous shot before she walked to the seat. (00:56:55)
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)
Answer: It was indeed Pazuzu, he wanted Regan to believe he was some friendly entity to gain her trust. Thus the Captain Howdy facade.