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.
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.
Factual error: Towards the end of the film Watney is told to discard the heavy nose cone of the Martian Ascent Vehicle and replace it with a flimsy plastic sheet because the atmosphere is so thin that it will not be damaged despite the vehicle being accelerated to Martian escape velocity - nearly 14,000 kmh. But the storm caused massive damage earlier. It cannot work both ways - if the atmosphere is so thin that it won't dislodge a jury rigged plastic canopy from an accelerating spacecraft, it cannot possibly whip up a storm like the one we see.
Plot hole: Rich Purnell started his calculations that required the Hermes to dock with the Tieyang Shen well before Teddy, the Director of NASA, found out about the confidential information about the Tieyang Shen even having enough fuel to be the booster.
Other mistake: When Matt Damon is brought back onto the Hermes, he is surrounded by his crewmates who are not in spacesuits. All air from the Hermes outside the control room had been expelled by the explosion, and could not have been replaced in the recovery time frame.