A character mentions the ship using parachutes, yet when it lands no parachutes are seen.
There are several close-up scenes of crying (e.g. at 21:30 Cmdr. Green crying). When at zero g, tears do not flow down the cheeks but rather accumulate at the eyes.
As angular momentum is always conserved, it is impossible to stop the rotation of the sleeping pods without getting the entire ship to rotate.
The Martian Moons appear far too large in the sky when they are seen from the surface of Mars.
A 20 minute time delay from Mars is shown. In fact a radio transmission from there would take a little over 3.5 minutes to reach the Earth.