To “Three Billboards” admirers and to the Hollywood Foreign Press Association, the outfit that hands out the Golden Globes, something about the movie rings true or feels timely. That presumption of truth is driving some of the annoyance over this movie. My favorite bad thing about “Three Billboards” is its ambition to play around with America’s ideological and geographical toys.

One of the toys is the word “nigger.” Another is the concept of political correctness. There’s a scene between Mildred and a hotheaded dimwit cop — the racist — named Jason (Sam Rockwell), in which she baits his racism by calling him a “nigger torturer.” He hits the roof. “Person-of-color-torturing” is what Jason says you must call it now, with exasperated lament. They volley the word and poke fun at its impropriety. You can tell that Mr. McDonagh relished the application of absurdism to the political correction (he knows “person-of-color-torturing” really is linguistic torture, maybe even for a person of color). But he also seems to like the loaded nonsense in the sound of the word “nigger.” What you hear in a scene like this is a kind of careless virtuosity. It’s a fun scene that’s sunk by how much fun it’s having with things you’re not supposed to have fun with. The whole movie is like that — it’s like Mildred — rude for sport and proud of it.

There’s certainly a place for a white artist to poke, laughingly, at our racial and class messes. (Mel Brooks, for instance, excelled at it.) But Mr. McDonagh doesn’t want to do more than poke. The Danish director Lars von Trier tried a more explicit damnation of the United States with “Dogville” (2003) and “Manderlay” (2005). But I liked the nihilism in Mr. von Trier’s respective approximations of racism and slavery, even if he followed a European habit, especially in documentaries, of diagnosing America’s ills in the least surprising and most patronizing way.

For a movie that asks you to behold so much violence — defenestration and talk of rape, a bludgeoning, a suicide, charred skin, a dental drill that treats a thumb like drywall — “Three Billboards” feels weirdly benign. Its black comedy doesn’t leave a bruise. The violence curdles into the cartoonish. The movie could be about grace and vengeance, but they’re presented as hoary lessons and hokey contrivances — happening upon a deer, sharing your orange juice with the madman who tried to murder you, juxtaposing the reading of an inspirational letter with an inferno. There’s no reckoning with anything, no introspection, just escalating mayhem. The mix of the silly and the serious puts the movie in Coen brothers territory. But they can adjust the settings for their cynicism. Even at their worst, they’ve got their finesse. Mr. McDonagh just keeps bashing away.