There are some very good things about this film. One is that someone pedantic was in charge of the titles and as a result the rule that prepositions are not capitalised is observed in the film's name onscreen. Another - the one that carries the film almost entirely - is Frances McDormand's performance. She excels as a tough woman who has had enough and takes on authority and anyone else who stands in her way.
What I didn't like about the film though was its uneven tone. Was it a black comedy? Was it a whodunnit? Was it a tearjerker? In the end, it was more of a cartoon, with the characters all drawn very, very broad.
There was Woody Harrelson, the good father and family man, with the emetically honey-lit wife and two ickle-pickle daughters - there was nothing believable about anything in this peculiarly luxurious - given the guy was on a policeman's salary - set-up, including the fact that Harrelson looked fatter and more glowing than I've ever seen him before, yet was supposed to be wasting very swiftly away. There was the idiot police officer who we were supposed to believe had a heart of gold, despite being a very violent thug. There was the dwarf who definitely had a heart of gold, and the attractive black woman and attractive black man, who, as soon as they saw each other ,understood that unwritten segregation laws meant that they must end up together and never consider the possibility of any kind of mixed race relationship.
Worst of all, from my point of view as a female, while there was a strong lead female character - McDormand - the rest of the female characters were excruciating. The writer of this film appears to think that the majority of womankind are laughable air heads - viz the girl at the agency that rents out billboards, McDormand's ex-husband's new girlfriend, and Woody Harrelson's wife, who, while not totally ditzy is essentially a cypher, (and also played pretty embarrassingly badly by Abby Cornish, but what could she do with that part, to be fair?) - or alcoholic son-castrators. Even the main character rather loses the moral high ground, when she decides to throw half a dozen Molotov cocktails at the town's police station without making absolutely sure that no one is still inside.
But it may be that the world of the film is one that has no morality. This would certainly help explain the ending, when Frances McDormand sets off with the idiot police officer, (who we are also encouraged to see as not that bad, even though we have been told he beats up black people and we have watched him kick and punch one character, throw him out of a second storey window and then dash downstairs, socking a receptionist in the jaw on the way, and continue kicking his victim in the middle of the town's main street) on what may or may not be a journey of possibly misplaced vengeance.
I suspect the film's mingling of jocularity and violence may be something that has been borrowed from Tarantino. I've never been able to bring myself to watch one of Tarantino's films, because I can't look at violence. Therefore, I'm totally unqualified to comment on their virtues or the lack of them. I can only say that, while I never got bored during Three Billboards, I did have to look away a lot. Afterwards I found it hard to work out how its mix of violence and grief and cartoon narrative, (with a tiny dose of possibly tongue-in -cheek schmaltz in the scenes involving Harrelson's family) really ended up knitting into a coherent whole. But, as someone who could never watch Tom and Jerry, because those awful moments when something heavy got smashed down on a cartoon creature's head made me wince too much, I think I may be way out of step with the great majority of cinemagoers. Despite being riveted by Frances McDormand's astonishing tour de force, I actually think this film is a load of old rubbish that doesn't amount to a hill of beans.