This film is far better than you might expect. It seems a shame that the film didn't share the title of the book on which it was based, 'Legion'; the present title brings to mind the countless abysmal horror sequels swamping the genre, an association this movie does not deserve.
'Exorcist III' is written and directed by William Peter Blatty, writer of the original film and of the fantastic yet sadly underrated cult classic 'The Ninth Configuration'. Unlike 'Exorcist II' (which was not penned by Blatty), the plot does not revolve around Regan, the little girl possessed in the first film. Instead, it involves the investigations of Lt. Kinderman (played by Lee J. Cobb in the first film, here played by George C. Scott). He is looking into a series of grisly, ritualistic murders which appear to be linked to a psychotic mental patient with a striking resemblance to Damien Karras, the tormented priest who played a central role in the first film (played again here by Jason Miller).
The plot is complex and intelligent - its links to the original are ingenious and moving, returning faithfully to characters from the first film. Because of this aspect, it certainly helps to be familiar with the original.
The only false note is struck by the film's most explicit link to the first two movies - the eventual exorcism. It simply doesn't seem necessary, with the priest played by Nicol Williamson a largely redundant character. It is rumoured that the studio forced Blatty to include an exorcism scene - if this is the case, it certainly shows, as the climax of the movie seems a little messy and rushed, compared with what went before.
Overall it's a 7/10 movie (as it's out of five for amazon I've been generous with the mark)- an unexpectedly clever, witty, and in places terrifying treat, and well worth a look, in spite of the flaws.