This is the Martin Scorsese adaption of the Dennis Lehane novel, set in 1954, with Leonardo DiCaprio playing the main character, U.S. Marshall Teddy Daniels. I read the novel (and am rapidly catching up on Lehane's entire back list) and thought it was quite good as a psychological mystery, with a twist ending that I didn't see coming. The plot has Daniels and his (new) partner taking the ferry (the book and movie opens with them on the ferry, with Daniels being sea sick) to Shutter Island, where there is a penal institution for the criminally insane. There is an escaped patient (disappearing from a locked room, and trapped on an island with only a single way off), and the marshalls are called in to find her. Daniels has an additional reason to be there, since he believes that one of the patients is the arsonist that was responsible for the fire that killed Daniels' wife.
The movie ends up being disappointing to me. Scorsese makes it appear as Gothic horror, with Daniels seeing visions (his dead wife and a child, memories of his war experiences in liberating Dachau), and the institution appearing menacing (including an isolated lighthouse, where Daniels believes experimental surgeries are taking place). It's quite clear early that Daniels has problems, where the book seemed to draw out the suspense a bit more (though I don't think you could figure out the final twist in either book or movie).
Both book and movie do address some of the issue with treatment of mentally ill patients (the head psychiatrist, played by Ben Kingsley, believes that with the right care he can possibly cure patients, instead of using lobotomies or drugs)