What is up with that shadow figure that glides by Regan's window when Kinderman was watching it from his car? That was creepy as fuck. Can you imagine being up there with a ladder and peeking into her window at the same time that happened? What would you see?
I can't help but think if the demon can untie itself, why not kill everybody in the house like she did to Burke? If it had done that, the possibility of an exorcism would've been decreased greatly and could've prolonged it's fun! I don't understand Pazuzu's logic here. I understand wanting revenge against Merrin but he's dying anyways.
The demon doesn't want to kill everybody. He killed Burke as a way to get Chris to get an Exorcism. He wants Merrin to come as he wants all the people in the house to suffer by torturing Regan. He unties himself later on screen during the levitation.
By having an exorcism, Pazuzu just shot himself in the foot IMO because it became his undoing. I think he should've thought things through a little more! He still could've tortured Regan(after killing her family) in an asylum while tormenting all the medical staff and expanding his evil. I think he should've had a better plan than just simply fucking around with a family, that's not gonna last! It's just the demon's logic seems very shallow and prideful to me, he could've done more than just being a sadistic asshole to the McNeil household. Maybe that's the point of the film.....evil has no real logic, just chaos and destruction. Just something to ponder!
Maybe I'm wrong and I might be thinking outside the box but I couldn't help but think that Reagan's spirit temporary left her body and escaped the demon. The shadow was Reagan's spirit (or ghost) moving around the room.
It also could be other demons lurking in her room as well, when Karras plays the tape recording we can hear other voices in the recording arguing with each other about Regan's fate clearly indicating there are other entities involved with her possession, not just Pazuzu. The commentary talks about that.
Listen to William Friedkin's commentary on the director's cut when they get to the scene where Karras is listening to the tape after finding out it's really English, he indicates multiple demons are debating what to do with Regan and some of the demons are clearly terrified of Father Merrin showing up and each voice sounds kinda different if you listen carefully. It's really bizarre and messed up!