When Kinderman connects the murder victims in this film to the case in the first movie, it is revealed that one victim, the African American boy, is connected because it was his mother that determined that Reagan was speaking backward English. However, when you watch the first movie, the person that determines the language is a man that is Caucasian.
During the breakfast conversation between Father Dyer and the university president there is an old man heading very slowly for the buffet behind the university president. And after cut and reverse cut he disappeared completely.
The size of the bandage and the tape across James Venamun's nose changes size several times.
Around 1h8m mark where the detective is talking with the nurse after hitting the suspect and bandaging his hand, she pulls out a cigarette and an additional cigarette falls out of the pack, onto her desk. In the next cut, the extra cigarette is gone.
The gruesome head cutting scissors were made for the movie and do not exist in real life. It is said in the movie that the scissors are spring loaded, so it takes very little effort to open them, but they produce a vicious force when being closed. This is not possible: the spring cannot produce more force when closing as it would take you to open it.
When the young boy is submitted to the neurology a nurse is spelling his last name. His last name starts with a "K" which is a crucial hint that he might be a next victim of the Gemini Killer.
In the German dub, however, they spell his last name as "Müller". Obviously the translators didn't get the hint.
The precise delineation of the effects of certain drug dosages: "A fraction less, and there's no effect, a fraction more, instant death" are complete Hollywood BS - everyone reacts uniquely to varying dosages of different drugs, so exactly precise measurement of a "fatal dose of a drug is questionable. For a detailed example of such, look up the murder prosecution of William Palmer (1824 -1856).
At the very beginning of the movie, the demon appears to address a Roman Catholic priest as "preacher", which would be a completely inappropriate form of address. A simple parochial priest would be "Father", and then the address would change with respect to increasing rank. The term "preacher" is very much a Protestant usage, and completely out of key with the whole ethos of The Exorcist and its sequels, even though, if memory serves, the original inspiration for The Exorcist involved a Protestant family and clergy.
When "Nurse X" hits the police officer, we can see a cable hooked to him when he flies back against the wall.
The buildings depicted as being Georgetown University Hospital in the film occupy a block near the school's main campus. They actually housed the hospital from 1898 to 1930. However, after that, the hospital moved to a much larger campus a few blocks northwest. At the time of filming, the old hospital complex housed a variety of non-medical activities, and its internal geography bore no relation to the interiors depicted in the film. The hospital room where Kinderman views the blood vials is located, judging from its view, where a student apartment was in real life. The corridor outside the room would have run through a wall into an adjoining classroom building. The interior decor of the hospital is based on Georgetown's student center, which represented the hospital in some location shots.
Dr. Temple (Scott Wilson) is perpetually seen sucking on a cigarette, but he never exhales any smoke.
The car chase completely mixes up the geography of Georgetown.
The movie suggests that Kinderman and Father Karras/Patient X were longtime friends, but they only met once in the original film, and their meeting could hardly be called cordial.