He links to a recent article by The Exorcist director William Freidkin, who visited (out of curiosity, really) the Vatican exorcist to see how accurately his film reflected real life exorcisms. I don't find the case he follows particularly convincing of anything, but one of the stories a New York psychiatrist tells him is more interesting:
LIEBERMAN: I’ve never believed in ghosts or that stuff, but I’ve had a couple of cases, one in particular that really just gave me pause. This was a young girl, in her 20s, from a Catholic family in Brooklyn, and she was referred to me with schizophrenia, and she definitely had bizarre and psychotic-like behavior, disorganized thinking, disturbed attention, hallucinations, but it wasn’t classic schizophrenic phenomenology. And she responded to nothing,” he added with emphasis. “Usually you get some response. But there was no response. We started to do family therapy. All of a sudden, some strange things started happening, accidents, hearing things. I wasn’t thinking anything of it, but this unfolded over months. One night, I went to see her and then conferred with a colleague, and afterwards I went home, and there was a kind of a blue light in the house, and all of a sudden I had this piercing pain in my head, and I called my colleague, and she had the same thing, and this was really weird. The girl’s family was prone to superstition, and they may have mentioned demon possession or something like that, but I obviously didn’t believe it, but when this happened I just got completely freaked out. It wasn’t a psychiatric disorder—you want to call it a spiritual possession, but somehow, like in The Exorcist, we were the enemy. This was basically a battle between the doctors and whatever it was that afflicted the individual.As for The Exorcist itself: I think I have mentioned before that I have never watched more than perhaps 10 minutes of it on TV, and found it too over the top to be scary or convincing. It's a pity, in a way, that the book/movie did this; from what I have read (a long time ago, now) cases of possession with much more subtle aspects could be much more persuasive of the supernatural.