Great quality cinema. A good starting idea, a good rythm throughout the whole thing, it looks good, but mostly: lots of great actors with well built characters. That's really the strong point, the crime part is just a pretext to make these characters interact, nothing much evolves on this front, and every character is interesting in its own way. Well apart, from the son that is basically useless. Even the dumb Penelope is way better as the comic relief.

The story centers first on McDormand's Mildred, she stays the main character, but the simplest and the most constant. Great performance as usual though.
Then the most interesting part comes with the sheriff, the most interesting character to me, and [spoiler]his death[/spoiler] relaunches the whole movie when it could have started to run in circles, also giving him a whole new dimension.
Then the story centers on Rockwell's Jason, who would arguably be the most changing character, but also the most cliché one. Just the drunk, violent, asshole cop that is not so bad inside and tries to be better, but yeah, still an asshole. [spoiler]Actually how come he's not already in prison during that third act ?[/spoiler]
Then a lot of supporting characters that all add something to the whole, even if some are there just for a single scene.

An interesting point is that in the beginning you wonder who will turn out to be the good guy of the story, because they all seem bad. Mildred may be grieving her daughter, but boy are her views extremes ! And by the end, there is not really a good or bad side to the story. Well I'd say that [spoiler]the sheriff[/spoiler] turns out to be a real good guy though, compared to the others.

Even if the main story does not evolve much during the movie, there are lots of shocking and unexpected events that keep you interested in what happens next, quite regularly in fact, this gives a quite interesting rythm comapred to what you would expect from a drama.

And of course, despite all being mostly tragic, it's expertly seasoned with whole sort of humourus scenes, light, dark, stupid, cute, a large spectrum of comedy that are even more memorable than the tragic parts.