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.
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 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.
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.
When Fred is boarding the Shuttle, he does so on his own, as the other two astronauts are already on board. This is incorrect as all three astronauts would board the Shuttle at the same time, as they would with a real mission.
When the crew first experiences weightlessness there are engine sounds in the background. Despite the fact that they are the sounds of jet engines instead of rocket engines it is clear that at this time the craft's 3 main engines are still firing, so the crew would not be weightless.
It takes radio signals almost 20 minutes to reach Mars, yet instantaneous communication happens throughout the film. However, this is clearly intentional because a forty-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 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".
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.
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.
Right when the ship reaches outer space, zero gravity 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.