I didn't notice any specific time references, but the film is clearly meant to be set in the near future. There's a lot of implied technology advances, enough to get manned missions to Mars with some pretty advanced survival gear. But it stops well short of near-magical technology like warp drives or teleportation. With the assumption of slightly-advanced technology, it's pretty easy to suspend disbelief over some of the less probable activities that happen in the course of the film.
Outside of the space program, the world is clearly recognizable as a mirror of our own. NASA still has to deal with Congress and public opinion, China is a rival on the world stage, crowds gather in Times Square, and so on. The politics and public opinion have some pretty major impacts, affecting the decisions made on the way to the rescue mission. One bit in particular stood out for me - when the Chinese space program officials decide to keep communication "scientist to scientist" rather than get the politicians involved. A none-too-subtle jab at the likelihood of international cooperation in the political arena, even in an emergency situation.
Matt Damon was excellent as the stranded Mark Watney, which is a good thing since he has a whole lot of screen time with no one else around. I also really liked Jeff Daniels as NASA Director Teddy Sanders. That character has to make some really hard decisions, and though he comes off as the bad guy in some ways, I thought Daniels' portrayal conveyed a real desire to do the right thing for the space program as a whole.
The effort put together to rescue the stranded astronaut is massive, which I think the film captures as well as possible in a limited time. There are a lot of references to how much work NASA has to put in with the rescue mission, some comments about the astronomical cost, and the Chinese program loses a planned mission as well. Many months are covered in the space of a couple of hours, which is never easy to properly convey in a way that feels real to the audience. There's one huge multi-month jump near the end of the movie, but other than that the movement of time is handled pretty smoothly.
In the end, the whole world is watching and cheering on the rescue mission. I didn't notice any direct reference to this in the film, but it struck me that there were probably thousands of people on Earth dying preventable deaths while the world was focused on the spectacle on Mars. Perhaps there's a bit of subtext there that isn't explicitly stated - it's amazing what can be accomplished with dedicated effort and resources, but only if they can be brought to bear.
I'm glad that I had the chance to watch The Martian. Well worth spending 2.5 hours to see.
