When Bill eats the stuff in tube that turns out to be hemorrhoid cream, he looks at the tube to read it, and the tube is all bent and squashed. From the camera angle looking straight at the tube, it is perfectly straight, no dents, and the cap is still attached.
When the team says they've landed, NASA crew claps and the screen shows they are midway from landing into Mars. Next shot, it shows they've successfully landed.
When Fred shakes hands with Bill, he is first shaking with his right hand, then his left.
In the isolation chamber, Randall's bunkmate's hair changes from combed to flat to frizzy.
When Fred starts braking wind in his space suit, Bill and Fred's helmets can be seen without glass, but later on you can see the reflection of the glass.
During the launch sequence, after the Solid Rocket Boosters separate, there is a shot of the first stage of a Saturn V falling away taken from the second stage. This is a completely different rocket.
When Fred arrives at work in his car there's not enough space to leave via either door so he goes out of the sun roof. Yet he's somehow able to remove one of the wheels which he wouldn't have been able to get any access to.
When the astronauts first step on Mars, they are in full daylight, but the sky is dark and stars are shining like on the Moon. This happens on the Moon because there is no atmosphere. Mars has an atmosphere and the daytime sky is reddish.
After the Solid Rocket Boosters separate, sounds of a jet engine can be heard in the cockpit. No rocket booster or spacecraft uses jet engines, which can only operate in an atmosphere in any case.
When Fred Randall and Gordon Peacock are in the isolation chambers, Fred's singing and talking can be heard in Gordon's chamber and there is light in the chambers. Isolation chambers have no windows or light and are insulated so no sound is audible.
The "6G" benchmark that a technician mentions just before Fred uses the centrifuge is not a continuity error; it is the previous record for the highest G-force sustained by an astronaut, not the highest G-force that the centrifuge can exert.
It takes radio signals almost 20 minutes to reach Mars, or according by the distance said in the movie: 35 million miles, 3 minutes to reach, yet instantaneous communication happens throughout the film. However, this is clearly intentional because a forty-minute or six minute time delay for each response during every conversation the crew has with Houston would only serve to make the film much, much, much longer and far more drawn out.
When Fred puts the American flag boxers up instead of the flag he puts the boxers up by the leg holes, and then when the camera changes angles the boxers are hanging up by the waist band.
In the scene where Randall leaves the Mars Lander to save Ulysses and Overbeck, Randall enters the airlock and goes off-screen. At that moment Julie turns around to look out the window of the Lander, but oddly enough, a grasshopper seems to be on the lower back of Julie's spacesuit.
When the Mars Shuttle is on the launchpad, it is obviously a model shuttle redesigned for the movie, with the name "Aries". When the shuttle launches it is clearly the real space shuttle, and in one scene during the launch you can see the name "Endeavour".
When Fred and Bill share oxygen in their spacesuits, the front shields of their helmets are not pulled down.
Right when the ship reaches outer space, zero gravity obviously takes over. But right as Fred Randall's arms start to float up, his earpiece falls out, obviously showing that the actors are just raising their arms on their own will.
When Fred is talking to Bud on the radio the night before the wind storm, he says "I'd be proud to end up like you", but his lips do not match the words being spoken.
In the scene in which the crew first goes into space and everything is weightless, Fred Randall turns his head to the right, thus knocking his ear-microphone loose, and it falls straight to the ground.