A lot of the science you'll see in the film is accurate: Matt Damon's character creates water using a dangerous (but real) chemical reaction involving rocket fuel. He grows potatoes using a realistically potent mash-up of Martian soil, water, and earthly bacteria. He runs around in a spacesuit that — while created by a costume designer who took some liberties — passed NASA muster, inasmuch as a movie suit can. The scenery on Mars is pretty accurate, too. Keep an eye out for the planet's misshapen moons. You'll hear people talk about a rescue mission taking four years, when the journey to Mars only takes six months — but that's because it takes a long time to safely plan and launch a crewed mission.
But it's Hollywood, so some stuff is less accurate. The storm you see in the trailer could never happen on Mars. You'll notice in some parts of the trailer that a door has been replaced with a plastic tarp — a fluttering mess of plastic and duct tape supposedly protecting our protagonist from the harsh world outside. That would probably work, because Mars has a really thin atmosphere — there's not a lot of wind out there. Unfortunately, in a world where a super storm could interrupt a human mission to Mars, that puny tarp would be useless. You can't have it both ways, Hollywood! Geez.
Other things to consider: Now that we're pretty certain that Mars's soil is full of briny water, the super-dangerous water extraction by way of rocket fuel combustion seems pretty silly. Should've stuck with the salty mud, dude.
My favorite fact check that didn't make the cut: Who the heck goes on a spacewalk without tethering to the ship?! No one, that's who. Go sit in the corner, Ridley Scott.
For more on why we loved "The Martian," check out our review.