Continuity mistake: In the shot where Matt Damon finally gets captured by his rescuer, he is face to face with the woman astronaut and when he smiles his upper teeth are Hollywood white. In earlier shots, his teeth were shown stained and nasty. Also, shots soon after the rescue "white upper teeth" shot again reveal stained teeth.
Continuity mistake: When Watney is putting duct tape on the plastic patch over the hole where the Hab airlock blew out, the first shot shows him outside the Hab putting the last strip in an evenly distributed set, from about the 10 o'clock position down to about the 4 o'clock position. Then (after a quick reverse shot from the interior), suddenly he is placing a new strip up from the 8 to 2 position, covering a spot that was already covered when he did the 10 to 4 strip, but which is now suddenly blank.
Other mistake: When Watney is in zero-g there are loose bolts floating around him. There is no way he would have left loose pieces in the MAV's cabin. Things left unsecured in microgravity tend to float around and damage delicate electronics. If something is not being used it's lashed down or secured in a cabinet. He has one chance to to get rescued and he wouldn't risk dying after over a year of surviving on Mars on something so foolish as unsecured equipment in the MAV cabin. He would have cleaned out every last bit of loose gear before launch.
Factual error: Teddy tells Purnell that he is the "director" of NASA. The chief of NASA is referred to as the administrator, not director.
Suggested correction: This could be a deliberate mistake. Is common in business for an "administrator" to be a clerical / entry level role (I've worked in such places). Referring to the character as Administrator of NASA could cause confusion in people not familiar with NASAs structure. By contrast, Director is likely to be understood by everyone as someone in charge, even if it's officially incorrect.
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)
Revealing mistake: When Mark builds his HAB greenhouse, he surrounds the growing area with sheet plastic. Later, when making his first attempt at lighting the hydrogen to produce water, there is a small explosion, which throws Mark back across the HAB. Given that an open-air explosion will produce a 360 degree shock wave, there should have been a noticeable disturbance to the plastic sheeting throughout the HAB, but the only disturbance we see to the plastic sheeting is the location where Mark is blown into it.
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)
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: 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: Upon arriving at the MAV, when Watney opens the door to exit the rover to head to the MAV, the home-made balloon on top of the rover does not deflate, as it should when interior pressure of the Rover is absent.
Continuity mistake: After Matt Damon has had to ration his food, a double who is thin and emaciated and whose face is not shown is used to replace Damon in some shots. But Damon's real upper body, as muscular and big as ever, can still be seen in some other shots.
Continuity mistake: When he pulls the metal out of his stomach, the wound changes position slightly to the left and back to the right.
Factual error: When we return to Watney waking up in the sand after the storm, the sands have various patterns and hollows in them which would have been erased by a storm that caused as much trouble as this one.
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)
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.
Suggested correction: I don't think that is correct. When he first comes up with the idea to reroute the Hermes back to Mars he was thinking about/ working on the calculations for the original probe before it blew up.
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.
Suggested correction: The first priority would have been to only replenish the air in the corridors leading from the bridge to the airlock, since these are the 2 locations the crew need access to. They did not need to replace all the air in the ship at once, just a relatively small area.
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: When Vincent draws the line on the Martian landscape picture and comes to the conclusion Mark is heading for Pathfinder, in the long shot, Mindy, who is standing next to Vincent, holds her left hand up by her face and her right arm down by her side. As Vincent begins to walk away, the camera instantly cuts to a close up of Mindy's face and now her right hand is up by her face and her left arm is down by her side.
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.
Other mistake: When Mark Watney is adjusting the solar panels of the path finder there are a few frames where he adjusts a small solar panel and you can see the actor is a completely different person.