I don't believe in reviewing over 10 pages, so here's my quick take on it...
I really enjoyed this film in general, I remember the story well because I'm an avid news reader, BUT.. .
Probably the biggest issue, (at least for me, and I'll leave the long-form reviewers write about the rest), was the casting. I found it incredibly cringe-worthy whenever Juliette Binoche was on screen, as if some tan makeup was going to make her Chilean, the Chilean Minister of Mining being a male model in his 20's, but most egregious of all was the godawful choice of Bog Gunton as president of Chile. Really??
We've all seen him in a dozen films and series playing the role of the power-hungry, overly ambitious and morally bankrupt politician, which he's always portrayed adequately but never amazing, but it was an incredible shame to cast him at all, never mind in the role of CHILEAN president!! It would take most viewers right out of the film, and especially make most cinephiles just cringe. I don't know what word would describe it better than that.
All that being said, it's a very enjoyable movie honouring the right kind of human cooperation and national effort. Too bad it was so much of a political stunt, without which opportunity the government of Chile would've let those miners die without batting an eye.