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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. (01:21:30 - 01:22:06)
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Trivia: Author and writer of the book and script William Peter Blatty has a cameo early in this film. He plays the producer trying to have a word with director Burke Dennings on the movie set before Burke turns his attention to Chris MacNeil. William Peter Blatty is the middle eastern-looking guy with the black hair and moustache, which is natural since his mother is originally from Lebanon.
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Revealing mistake: When Father Karras sprinkles holy water on Regan, they forgot to paint her ear lobes and it looks terrible. (01:32:30)
Answer: The demon wants everyone to lose hope for the girl and give up on her. Her father, having already flown the coop, just makes this goal that much easier.
TonyPH