Continuity mistake: During the montage where Watney is preparing the potatoes, there is a shot outside in his suit where he attaches a cable or hose to the MAV outside the habitat. You can see the large engines of the MAV above Watney's head and the letters "MAV" on the leg of the vehicle, as well as the remains of the wrecked Rover 1 next to it, right where Martinez left it. By this point in the story, the MAV has already departed the Ares III site. This is supposed to be the MDV - the Mars descent vehicle - and Watney refers to the MDV when he discusses where to get the hydrazine - but it is the bottom of the MAV that is shown.
Continuity mistake: When Bruce Ng is video calling Teddy Sanderson and Mitch Henderson to explain the modifications Watney will need to make to the Ares 4 MAV, there is a point in which the model MAV behind Bruce contains only a chair, all other chairs and the control console having been removed. Then, as Bruce and Mitch explain to Teddy that since Martinez will be remote-piloting the MAV, Watney doesn't need the controls, there is a shot of Bruce pulling several chairs and the control console out of the model.
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.
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.
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.