Other mistake: During the storm scene in the beginning of the movie, the astronauts' faces inside the helmets are brightly lit, meaning there's a light source pointed directly in their face. That's something that would render them mostly blind and unable to see and appears to be nothing but a dramatic effect for the camera. (00:05:00 - 00:08:00)
Character mistake: As Teddy is announcing the bad news, he calls Mark Watney 'Mark Watton'. (00:09:48)
Continuity mistake: Right after Matt Damon wakes up from the storm, while he goes back to the base, his costume has a small backpack with a "2" written on it. After he closes the second door the scene cuts and the backpack is gone. (00:12:25)
Continuity mistake: This mistake is in the extended edition: When Watney decides "I'm not going to die here", he packs up his five crew mates' belongings in plastic boxes and stows them in one of the two bottom bunk beds, from which the mattress has been removed. Then Watney is shown struggling out of bed, presumably the next morning, and a wide shot shows all six bunks. Every bed has a mattress and bedding on it and there are no boxes in sight. (00:19:10 - 00:19:50)
Factual error: During Watney's funeral, a Marine is carrying the United States Flag in what is supposed to be a multi-service color guard. In any joint ceremony, as the senior service, the Army always carries the National Colors and commands the color guard. (00:19:17)
Continuity mistake: Mark Watney is shown whittling the cross when he needs something to ignite to burn the hydrazine, the next shot the cross is intact. (00:26:18)
Suggested correction: It is possible Martinez brought more than one cross and the one Mark is holding while lying down isn't the one he was whittling just before.
Continuity mistake: When Watney decides to retrieve Pathfinder, the date is sol 79. On earth Vincent says Watney has been traveling in the same direction for 13 days, and maps Watney's position as about one quarter of the way to his target. However Watney's helmet readout shows him arriving on Sol 94, only 14 days after he probably left the hab on sol 80. (00:42:00 - 00:44:00)
Other mistake: When Vincent Kapoor first goes to JPL in Pasadena, he gets out of the car and the letters "JPL" are shown on the door. Since the shot is from the inside looking out at Kapoor, the letters should be backwards. No one labels a building for viewing from the inside. (00:43:00)
Factual error: Earth's moon is in the frame as a clear crescent after the explosion when Mark goes out. Mars' moons are not spherical, so can't appear like that. (01:10:00 - 01:11:00)
Character mistake: The flags (both USA and China) on Iris 2 when hung vertically, were hung incorrectly, and appeared as such on the cover of the "Times." They should have been "reversed" so that canton is still in the upper left hand corner. (01:30:35)
Continuity mistake: After breaking his helmet (with the "2" on the right side camera and with the name "Watney" on the back, he replaces it with one with no name and no number on the camera. However during the scene when he is preparing for the final trip, in shots of him manhandling solar arrays he has his old helmet on again. (01:34:25)
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.
Suggested correction: The plastic would certainly be flexing in and out because of the pressure of the wind gusts during the storm. We saw earlier that the gusts of the storms were strong enough to blow a suited explorer off their feet and push them across the surface. Let's say that the HAB is pressurized as much as it can be without blowing out of the plastic, tape, and bungees sealing the airlock. A storm gust would still be able to push the flexible plastic in momentarily, and it would pop back out after the gust passed.
The movie took liberties with the physics of Mars. The gusts on Mars wouldn't be able to blow over a person or a spaceship, let alone push them across the surface, but they needed it for the plot. But using the same physics they then have wedded themselves to, it could then be strong enough to cause the plastic to flap, even though in real life it wouldn't. This is more of a deliberate mistake than a factual error since the writers certainly knew what they did didn't match reality.
Except they didn't 'wed' themselves to their fictional physics. Towards the end of the film NASA tells Watney that a flimsy plastic covering on his ascent vehicle will not be dislodged on acceleration to Martian escape velocity because the atmosphere is too thin to cause any problems. That's cheating in anyone's books.
Factual error: When the crew is walking around the area of the Hermes with artificial gravity created by spinning the ship, the angle of the crew members' bodies should be perpendicular to the curved floor of the ship. However, in multiple shots, the crew standing at different locations of the room are seen standing at the same angle, directly upright.
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.
Suggested correction: The Hermes missions are much more long term than any current NASA missions. In this fictional future, we have no evidence that Beck is the only one qualified enough to carry out this rescue. Additionally, Lewis has the emotional connection, having been the one to instruct them to leave Watney on Mars.
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.
Other mistake: When devising the plan to retrieve Watney, it is mentioned that the Hermes crew have had to lash together all the webbing on board to make the longest possible tether. When this tether is used, there is no evidence of any lashing together or other extensions or modifications to lengthen it. The tether is one continuous length and is stored on a reel that was designed for the length of tether gathered on it.
Deliberate mistake: The atmosphere on Mars is only 1% as dense of that as Earth, so 175kph windstorms would feel like a light breeze. They would have very little effect on the astronauts or MAV. The writers of the book and the film were aware of this, it was a small cheat to let the rest of the story unfold.
Other mistake: Rich Purnell explains his plan to redirect the Hermes to Mars in order to rescue Watney, positioning people to represent planets and using a stapler to show the trajectory of the vessel. He is talking to experienced, qualified engineers and technologists working at a very high level on the space programme. They don't need drama school play acting to be understand things like this. He could have explained his plan in the most complex and abstruse terms and they would have been way ahead of him.
Suggested correction: This isn't really a mistake. Yes, the character oversimplified the explanation but, as is shown when the character is introduced, he doesn't exhibit typical social behaviour. To him it's probably normal to explain things that way to strangers (which is basically what the people he's talking to are).
I think this is one of those borderline mistakes. Movies and TV shows often have a character over-simplify things, especially when involving science, for the audiences' sake and not for any of the characters. This type of mistake is similar to when characters start a conversation, but the show skips time by having characters arrive at a new location in the next scene without showing them traveling, but then the characters continue their conversation for the audiences' sake.
Character mistake: In a scene when Watney is recording his video log, he imagines what would happen if his pressurized shelter suddenly would break. He concludes that he would implode, but the correct wording would be explode.
Continuity mistake: When he signs his name on the white sheet, his last day at the hab, he signs 'Watney' and underlines the name with the tail of the 'y'. Next shot where he walks away from that sheet, it's just a scribble signature.
