A mysterious serial killer with no identity (Jeff Goldblum) is captured and sent to a mental hospital, where a doctor tries to analyze him. Seems that the patient believes he is the devil, which the doctor initially scoffs at until his behavior slowly convinces her. Why would the devil allow himself to be captured? Because he wants to provoke her into killing him, in order to win some sort of victory over science and rationality.
Mister Frost is best when it sticks to the central premise of Satan (or a man who believes he is Satan) butting heads with a shrink. These scenes are taut and clever, playfully examining ideas of faith vs. science. Goldblum is, no surprise, fantastic in the role. He's charming, funny, creepy and brings his patented Goldblum oddness to the role, lending an otherworldly quality that I think few actors could match.
The film flounders whenever it strays. Subplots about Frost's possible influence over others, including inspiring a man to go on a shooting spree, are silly and boring, a distraction from the central drama. Personally, I also would have preferred more ambiguity. It's clear from relatively early on that Frost is the real deal and not just a clever kook, a mistake that saps some of the potential suspense and fun from the rest of the film.
I think Goldblum's scenery chewing is enough to recommend Mister Frost, but the film has a lot of potential in its premise that it does not live up to.