It's impressively acted, cleverly written. Didn't care for the ending. It was nominated for seven Oscars, and won two: Best Actress, Best Supporting Actor.
The Best Actress, Frances McDormand, is Mildred, about as far from Marge Gunderson as you can get and still identify as female. She's difficult, and events have made her more so: months back, her daughter was raped and murdered, and there's been zero progress in the investigation. So to draw attention to this miscarriage, she posts three … well, you see the movie's title. They are designed to let others feel her outrage. (And also make up for the guilt she feels.) The local cops are unhappy, because they know there's no magic spell that can turn zero leads into more than zero leads.
The main local cop, Willoughby (Woody Harrelson), is somewhat sympathetic, but he's got pancreatic cancer with a grim prognosis. One of his deputies, Dixon (Sam Rockwell, the other Oscar winner), is a real loose cannon, under a cloud of a torture allegation. (And, give subsequent events, that's an entirely credible allegation.)
The movie proceeds with considerable bad language, very black humor, occasional violence, shocking plot twists, and so on. And then… well, did I mention that I didn't care for the ending?
I searched for enlightenment using Google, and happened upon a New Yorker pre-Oscar essay on the movie by Tim Parks The Feel-Good Fallacies of “Three Billboards Outside Ebbing, Missouri”. Keeping in mind that "feel-good fallacies" you might share with a New Yorker writer might be the null set, I think he put his finger on something:
How does a film so empty of emotional intelligence, so devoid of any remotely honest observation of the society it purports to serve, sweep the board on prizes? This in a time when intolerance and gun violence are rife, when both would seem to demand a more serious response. “Three Billboards” gives us a world in which cleverness is all-important. All of the confrontations involve quips; the characters are intelligent only insofar as they know how to attack one another. But it goes deeper. In one of the few moments when the film attempts to suggest real grief on its heroine’s part, Mildred is sitting on the ground, having just witnessed the destruction of her billboards. Beaten, she weeps. Her head drops, she looks at her pink slippers, and the clever script, by the extremely clever [screenwriter/director Martin] McDonagh, has this distraught woman start a hell of a clever conversation between the two fluffy creatures on her feet about what she should do. Grief quickly dissolves into grim comedy, with one slipper deciding that the police had better watch out for Mildred’s response, and the other challenging her to live up to this bold claim. It is at once one of the slickest and sickest moments in a movie that constantly encourages its audience to believe that it is watching something serious while it is actually being fed a diet of eye candy, violence, and standard repartee.
Ouch! Part of this is Park's feeling that Our Times Call For … some different movies, I guess.