I recently saw Titicut Follies, the 1969 documentary film about the harrowing conditions in a Massachusetts prison for the criminally insane. The movie was banned by the state of Massachusetts until it was deemed unconstitutional in the late 80s. One of the subjects is a man who has been transferred from a regular prison to this mental facility. He is very clearly sane, and argues logically in his own defense.
I recently saw Babadook (No spoilers), a fantastic horror movie that was not only scary, but had a compelling, thought provoking, and grounded story to back up the supernatural.