Factual error: After Watney patches the blow out of one of the HAB's airlocks with plastic sheeting, tie down straps, and duct tape, he pressurizes the HAB and the plastic sheeting pushes out like an inflated balloon. Assuming the plastic and duct tape would hold this is correct, however the plastic would be much more taut given the pressure difference inside and outside. The real mistake is later in the scene during a sand storm the plastic flops in and out. The plastic would remain tautly inflated, since the inside pressure is much greater than outside, and since the HAB is airtight the storm would have no equalizing effect to cause the plastic to be sucked inward.
Factual error: When Commander Lewis in the tethered MMU jet-pack-chair is catching Mark Watney flying Iron-Man style via air jets from the hole in his glove, Mark misses Lewis' hand and grabs the tether, with some angular velocity relative to Lewis. As Lewis pulls the tether hand-over-hand to bring Mark closer, the angular momentum should spin them faster and faster like ice skaters pulling their arms in or Argentinian bolas (weighted balls connected by a cord) winding faster and faster around a target. Only when solid contact is made would Lewis' MMU be able to counteract the spin. The expected rotational speed-up effect is not seen.
Factual error: Lewis replaces Beck on the EVA to rescue Watney. On a NASA mission, each crewman is a specialist in several areas. While all of the crew have trained on EVA, Beck is the specialist for Ares III meaning he practiced EVA protocol and maneuvers 2-3 times as much as any other crew member. So while it is a nice dramatic moment for Lewis to replace him, a real mission commander would trust the best trained personnel to do their jobs, as she is actually lowering the chances of success by replacing Beck.Grumpy Scot
Trivia: The secret project created to use the Hermes to return to Mars to rescue Watney was called Project Elrond, a reference from the Lord of the Rings (also used in the original book of The Martian). Mitch Henderson, played by Sean Bean, was an attendee at the Project Elrond meeting. Sean Bean also played Boromir, who was an attendee at the Council of Elrond in the LOTR movie.Blathrop