I saw The Martian over the weekend and enjoyed it a lot. I particularly appreciated the fact that the plot did not lurch from one heart-stopping crisis to another. I won't belabor the science issues in the movie, since those have already been widely discussed on the Internet. The biggest one has to do with the Martian "storms." The atmosphere on Mars is so thin that it wouldn't be capable of the kind of death and destruction you see at the beginning of the movie.
Also, the gravity on Mars is much lower than on Earth, but this only becomes apparent near the end of the movie, when Matt Damon begins bouncing around a lot more. Or maybe he just lost a lot of weight from his starvation rations.
My biggest issues regarding realism have more to do with sociology than science. Why didn't NASA put communications equipment in the Mars habitat? This is a common feature of science fiction: the Technology that Must be Unrealistically Defective in order to advance the plot. The most famous example of this is in the short story "The Cold Equations," in which we are led to believe that a spaceship has such a low tolerance for extra weight that a small stowaway would make the planned flight impossible. When this is done well, of course, the reader doesn't even notice the swindle.
The other implausibility is the fact that only a low-level scientist, working on his own (with the aid of excessive coffee consumption) would come up with a new trajectory for the ship, one that evaded all of the best minds at NASA. NASA might do a lot of things wrong, but one thing they know exceptionally well is orbital mechanics, and they are intimately familiar with slingshot orbits. The only realistic thing about this is the excessive coffee consumption. I have been there (and still am).
Update: Several of you have pointed out that the poky thing sticking out of Matt Damon's abdomen was, in fact, the radio antenna, which was destroyed in the storm. So I stand corrected.