For the surface of Mars, the filmmakers shot in Moab, Utah, where they found giant cliffs, red rocks, a lack of vegetation, and the overall scale of what could be a distant planet.
The filmmakers spent nine weeks at the Johnson Space Center, in Houston, Texas, shooting at the famous Rocket Park (the gargantuan Building 9 that houses all of the spacecraft mock-ups for the ongoing shuttle missions) and Building 32, which houses the world's largest thermal vacuum chamber and simulates all conditions of outer space (except zero gravity).
When Randall is singing "He's got the whole world in his hands", on the world broadcast and starts faking singing in foreign languages, he says in French: "Je suis le papillon sur la table", which translates to "I am the butterfly on the table".
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.
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".
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.
Fred Randall: They say that when a mother's child is trapped the rush of her adrenaline gives her the strength of 20 men. Alright Commander call me Mommy!