Main problems and unanswered questions [spoilers]
The backstory with Clooney and his daughter made little sense, it wasn't really fleshed out. We see him as a young man being practically indifferent to his wife even as she announced she wasn't pregnant after all (a lie). There seemed to be nothing more going on than a guy too immersed in his work to pay attention.
No big blowup, no clashing over stupid things, the marriage just disintegrated - it's probably significant, although we don't know in what way, that the little girl's only spoken line in the entire movie, delivered in a dream, was "Did you love her?". A question they never answered. We don't know. Nor do we know why he followed his daughter growing up and her career without ever introducing himself. Did he love her? It seems like it. But his behavior and the whole family dysfunction seemed ... random. Unexplained and almost inexplicable. That bugged me.
"The Event" was never really explained either (which is not a fatal flaw by itself). Something set off a chain reaction that was poisoning the Earth's atmosphere. Yet they had a colony ship in orbit and even a month after The Event there were still a few clear areas with breathable air. How could they have been overwhelmed by poison gas so quickly that they couldn't load the colonists onto the rockets and send them up there? There were lunar bases and countless other spacecraft listed too - were they all decommissioned and unstaffed at the same time? It makes no sense that a civilization once they have that level of space infrastructure wouldn't have hundreds or thousands of people off planet at any one time. That's becoming a mantra isn't it? Doesn't make sense.
Never mind the Empire Strikes Back asteroid field stuff. Real meteor swarms are much sparser but each little rock hits with far more punch. Even as big as the spacecraft was, just a handful of rocks the size of the ones shown crashing into them should've crippled key systems - if not broken the vessel into pieces. Genetically, two people cannot repopulate the species. So either give them a big store of frozen embryos or have them collect off planet survivors before returning to Jupiter. What difference does it make if one couple and their child survive and that's it? It only postpones extinction by one generation.
I'm sorry, but they really SHOULD have had survivors from Earth. It's impossible to believe not one person made it off. Why not have the two astronauts who went down save their families and return? Give us something to cheer for amid the unrelenting sadness.
I was waiting for Clooney to at least say "I love you ... my daughter" (or words to that effect) before radio contact was lost. And get to see her reaction as she realized THAT'S why he always took an interest in her, gave her a moon rock as a gift. But nope. He stayed clammed up.
This movie was beautifully filmed and I really wanted to like it. But I ended up more frustrated than anything else. The obvious Adam and Eve in the Garden of Eden reference at the end was all the resolution we got to anything.