The harshest criticism I have for Cuarón's story, and James' before it, is that it's unremittingly, unreasonably, unrealistically grim. Where is the biotech industry in all this? Vague rumors of a secret project aren't enough; where are the millions of skilled workers, the trillions of dollars in R&D funding that would surely be directed at the problem? By injecting human DNA into the egg cells of pigs (or sheep, or some other mammal unaffected by the fertility apocalypse), we could clone large numbers of healthy children who would—after some respectable interval and an appropriate course of sex education—start reproducing the old-fashioned way. And while we're at it, why not improve their genomes a little, so this kind of thing never happens again? On the side, we could upload our consciousness into robot bodies, cross our DNA with that of the smartest apes, and of course create sterile dome cities where toxins and pathogens are ruthlessly scrubbed away.Given enough time and resources the human race probably could at least come up with some sort of stop-gap solution. Whether it would work to save our species is harder to know. Could we clone forever? Could we remove the toxins from the environment that caused the infertility in the first place? If there was a breakdown in civil order, perhaps not.
For another take on the same issues - use of technology (particularly cloning) to overcome the near destruction of the human race due to environmental catastrophe - I recommend reading Kate Wilhelm's Where Late the Sweet Birds Sang.