(at around 1h 16 mins) When Regan wakes up in hospital, she removes the IV needle from her arm, but in subsequent shots, there is no IV drip bag stand next to her bed.
The institution where Regan receives treatment has glass offices in which you can see the patients and their counselors with the only privacy being offered is by audio. Glass rooms in actual institutions usually have blinds/ curtains to provide visual privacy.
(at around 34 mins) There is a wide open gap on Regan's terrace where she almost falls off the building. No contractor or builder would ever agree to build a gap or remove a railing on a terrace like that for obvious reasons.
(at around 3 mins) At the start of the film, with the burning woman, she appears to have non-flammable hair.
In the flashbacks to Regan's exorcism by Father Merrin, in the original film Regan was wearing a blue nightgown for these scenes in The Exorcist (1973), but in Exorcist II: The Heretic (1977) Regan is depicted as wearing a white nightgown for those scenes.
(at around 1h 45 mins) When Dr. Tuskin is trying to help a burning Sharon, we hear her yell out "Sharon!" but her mouth never moves.
(at around 27 mins) When Fr. Lamont is showing Dr. Tuskin the drawing Regan had made of him on fire, Dr. Tuskin says "Where are you going?" but her lips don't move.
(at around 1h 45 mins) When Regan is watching Father Lamont give in to the Regan-demon, we hear her moan "No. Please." But her mouth doesn't form the word 'Please'.
In one of the rooftop sequences with Regan, a reflection of the camera operator's hand can be seen in one of the many reflective surfaces.
(at around 36 mins) When the two characters return to the house in Georgetown, they are in the pouring rain holding wet umbrellas which clearly reflect the very intense white film lights above them.