Factual error: Another of the film's misunderstandings of how Mars1's 'artificial gravity' would have functioned: When Mars1 power is lost, loose items start to float. As the 'gravity' was obtained by the centripetal forces of the rings' rotation and not by some kind of Star Trek graviton generators , items would have initially retained their inertia and ended up against one of the end walls. Also, when the rings were restarted, the same items would have probably ended up at the opposite wall and then have been forced down to the 'floor' instead of suddenly dropping to the floor.
Factual error: When Gallagher is lifting off in the Russian ship, the stars behind him move like he's travelling at warp speed. The only (realistic) way the stars would appear to move so fast is if he was spinning around rapidly. In that lift-off scene, the stars should appear immobile or barely moving as the ship rotates into position in orbit.
Factual error: The ice storm results in, amongst other things, driving white snow. As terraforming has not had the chance to bind Mars' surface dust into anything denser, the result of the ice storm would be very red tinted by the dust. This happens on earth, eg after volcanic eruptions. It would definitely not be almost pure white, and visibility would be zero.
Factual error: Misunderstanding of centripetal acceleration. When the ship accelerates out of orbit early in the movie the rings are spinning to create artificial gravity (agrav). Using this method agrav gets weaker nearer the hub of the rotating section, yet, with the exception of the "stand him up" error already mentioned, agrav seems to be the same throughout the ship when the rings are spinning. When the ship loses power the agrav is gone immediately, and when power returns it comes back immediately, but this can't happen with a spinning ship. The ship and everything in it has angular momentum. That doesn't just go away. The rings will continue spinning and agrav will remain. If there are brakes to slow the rings down anything not secured (people, silverware, etc.) will continue in the direction of spin until it impacts something. To people inside it would seem as if the floor moved out from under them and the walls came over to hit them. When the rings start spinning again agrav doesn't just return and everything just fall to the floor. The agrav will increase with the spin rate. Anything/one floating will not be affected by the spinning until coming in contact with something connected to the walls of the ring. If there are no walls except the outer hull, around the ring where they are they will float until the air, which is slowly accelerated by the spinning ring, pushes them to the floor.
Factual error: Why would an interplanetary probe have a touchscreen interface with a voice synthesizer? It was sent to Mars and there was no reason to believe it would ever be seen by a person again (the sample return thing did not contain the screen - it was in the main body). All programming can take place remotely by radio. Lastly, adding such superfluous equipment would have been horribly expensive - it takes tens of thousands of dollars to boost just one pound of material into low Earth orbit, let alone onto a course for Mars.
Factual error: When the scientists kludge together a radio to talk to their orbiting spaceship, they are shown ripping the guts from the Mars rover. The small RF transmitter used in the rover is described by NASA's website as only having the range of a 'walkie-talkie' (since it's only used to talk to the lander), with a max range of some 400 meters, not designed to communicate with orbiting assets. Also, the UHF modems in the lander and rover were "modems", not designed to modulate voice signals, or even receive them. Even Aricebo wouldn't be sensitive enough to "hear" those UHF radios, even if it was pointing at Mars. They should have used its Auxiliary Transmitter, if they had an adequate power source. Suspension of disbelief on this point is stretched a little far - the plot would have been better served if the characters referred to a fictional lander, with the hardware better suited to the plot.
Factual error: Yet another problem with Mars 1's artificial gravity. It has two spinning rings to produce artificial gravity - as the rings spin, they push up on objects inside them that try to move in a straight line due to inertia. However, gravity is consistently experienced in areas other than these rings, such as the landing vehicle or the bridge. The rings also seem far to small to contain any sizable living space.
Factual error: When the Mars 1 Ground crew rigs a radio transmitter, somehow, Earth receives the signal and radios back to Mars 1 that they have "received a signal on a frequency not used in 50 years". We've already established that Mars 1 requires 40 minutes to send and receive a radio signal. How could Earth receive a signal so faint from a handheld radio?