If you saw a trailer for The Martian, you probably already got the gist of the movie. The Ares III mission (third in a series of five manned mission to Mars) encounters a mission-scrubbing sandstorm only twelve days into their mission. During the emergency evacuation one crew member (Mark Watney) gets lost in the sandstorm after getting hit by a flying communications antenna and is (quite reasonably) presumed dead after his suit reports a suit breach, leading the rest of the crew to abandon Mars and head back to Earth. Mark turns out to be alive, amazingly (the blood from where he got impaled having sealed the small hole in his suit), and most of the rest of the movie deals with his attempts to survive until he can be rescued. Luckily, as this was a series of planned missions, Ares IV is already set to land 3800 kilometers from his position in a few years, leading to the idea of getting there to meet it when it arrives. The rations left behind in the evacuation won't stretch that long, but a serendipitous discovery of viable potatoes among the rations leads to him growing them and giving hope that he can survive long enough to modify the rover (also left behind) to be capable of traveling to the landing site.
It takes a few months for anyone to notice he's still alive based on satellite photos of Mars, but when they do they manage to get communications up and running between NASA and Mark. NASA fast-tracks sending the scheduled pre-delivery of food for the Ares IV mission in order to get it to Mark faster, especially after a freak explosion blows up his growing habitat and destroys his potato crop, leaving him with the unenviable prospect of running out of food in a very definite amount of time.
Meanwhile, the rest of the crew of the Ares III are still on their several-month journey back to Earth in the Hermes crew vessel. An astrodynamicist at NASA realizes that the Hermes could potentially slingshot around Earth and get back to Mars fast enough to save Mark as a backup in case the food shipment doesn't make it. (Turns out the Ares IV ascent vehicle has already been landed at the proposed landing site on Mars, since it could be launched ahead of time and means the actual Ares IV mission doesn't need to bother with bringing it along; Mark could take it up and rendezvous with the Hermes as it slingshots again around Mars on its way back to Earth.) This idea is floated in a secret meeting, but is rejected for putting the rest of the crew in additional danger (not to mention several more months of spaceflight time). However, when the rocket carrying the food package explodes during launch the Ares III mission director secretly sends the crew details of the maneuver, whereupon they unanimously vote to mutiny and perform the maneuver against NASA's orders.
Ultimately, the Hermes makes it back to Mars in time for Mark to make it to the Ares IV ascent vehicle before starving, where he strips a frankly ludicrous amount of material out of the ascent vehicle in order to make it light enough to reach the speed necessary to rendezvous with the Hermes (as in, he strips out all of the manual controls leaving it controlled remotely from the Hermes, and even the windows and airlock, performing the ascent in his spacesuit with a tarp over the windows). After a climactic rescue scene Mark is saved, and in the epilogue it's shown that everyone made it back to Earth safely and Mark has taken up teaching future astronauts.
Think Apollo 13 meets Robinson Crusoe.
Now, most of the time, the science was quite good, as you would hope for a movie where almost all of the tension comes from butting up against the laws of nature. Things like burning hydrogen to get water (and causing an explosion due to unaccounted-for excess oxygen), space scenes shot in zero-g conditions (although the Hermes also has rotating sections where people can walk around normally due to centrifugal force), and a homemade bomb made of sugar mentioned as being “four times more powerful than a stick of dynamite” (which is entirely believable, given the vast amounts of energy in food; thankfully, it doesn't easily burn fast enough to explode under normal conditions). The shots of Mars were also particularly gorgeous, especially in the 3D version I saw, which worked well; the 3D was used to good effect rather than being a mere gimmick, and was never used to “in your face” type things.
As an astronomer, however, several details stuck out to me while watching. At least twice, the Martian night sky is shown with a small crescent moon hanging in space. While pretty, it's also unrealistic because Mars' two moons Phobos and Deimos are both tiny, and far too small to be seen as anything other than star-like points (they're also irregularly shaped like asteroids, so they wouldn't have a nice crescent like the Moon does here on Earth). There was also a beautiful shot of a Martian sunset…which looked suspiciously like a sunset on Earth, with a blue sky fading to red around the Sun. Interestingly, it's almost the exact opposite on Mars: the sky is normally red due to ever-present dust in the atmosphere, while fading to blue around the Sun at sunset and sunrise. The atmosphere on Mars is only about 1% as thick as Earth's at ground level, so it's usually too thin for there to be enough Rayleigh scattering to produce the blue skies here on Earth. However, at sunrise or sunset the Sun's light passes through enough of the Martian atmosphere to create a pale blue color, as seen in the picture below. (On Earth the extra atmosphere at those time scatters so much blue light out that what's left appears red or orange.)
Another thing I noticed is that the movie tries to have it both ways with regards to how thick Mars' atmosphere is. In the first few minutes of the movie, the sandstorm that kicks everything off both rips off a communication dish and takes out Mark with it, and presents a credible threat of blowing over the ascent vehicle. Yet near the end of the film as Mark is preparing to ride an Ares IV ascent vehicle that has had even its windows and airlock removed in order to lighten it, it's pointed out that the Martian atmosphere is thin enough that you could feasibly pull such a thing off due to air resistance being essentially non-existent. I'm not familiar enough with the fluid dynamics of the Martian atmosphere to say anything myself, but I've read that in reality even a fierce sandstorm on Mars would feel like a light breeze and wouldn't be able to tip over a large metal ship. The highest atmospheric density on Mars is only 0.6% that of Earth's, so I believe it. Mars' famous planet-wide sandstorms work because of the lower Martian gravity, not because the wind is so strong. And speaking of gravity…
…as a physicist, I couldn't help but notice how Mars has Earth gravity the whole time. The surface gravity on Mars is just 3.7 m/s², a mere 37.6% of Earth's 9.8 m/s². Obviously the movie was filmed on Earth (Wadi Rum in Jordan standing in for Mars), and it'd be to impossible to change something like that, so this isn't a fault of the movie in any way—it just wouldn't be possible to make it look realistic. The fact that something so minor is what I kept noticing really says something about how good the rest of the science was.
Interestingly, during the part where the crew on board the Hermes votes to mutiny and perform the maneuver to return to Mars against NASA's orders to save Mark, the commander says something to the effect of “if we do this, none of us are likely to ever fly again.” This may sound like mere dramatic oratory (although it's justified in the context), but it turns out this has actually happened: in at least two cases crews of astronauts (on Apollo 7 and Skylab 4) have mutinied while in space, and both times no one on the crew ever flew in space again, as eloquently explained in the videos below.
Overall, as I said, I found it a pretty good film, though I couldn't watch the early scene where Mark performs self-surgery to remove a bit of metal from his abdomen from where a spike on the communication array impaled him with nothing but local anesthetic (queasiness is why I'm an astronomer and not a doctor!). I laughed at the part where, in the secret meeting to explain the maneuver for the Hermes, the guy who came up with the maneuver calls it “Project Elrond” and while one of the people in the meeting is trying to figure out what “Elrond” means the normally staid and stoic director of NASA pipes up from the background to say “If this is the council of Elrond, I want my code name to be Glorfindel.” And I especially winced in sympathy at Mark's line “I ran out of ketchup seven days ago” said while eating a potato. Surely that would have to be the worst thing about being stranded on Mars: running out of ketchup. A hui hou!