Deliberate mistake: At the end of the movie Rocketman shows his lady friend a space blanket, out of which he states he made something: ballroom dancing outfits. The difference in the material is just too obvious for this not to be a deliberate mistake. The outfits aren't the slightest bit related to the foil they were supposed to be made of.
Continuity mistake: In the press conference scene, before they announce the new astronaut, there are a couple of shots of Fred and Gordo sitting next to each other. In those shots they each have a microphone right in front of them. However, just as they are about to make the announcement, Gordo's microphone has moved, and he has to slide it over to be in front of him.
Revealing mistake: When Fred Randall is in the motion sickness machine (the one that spins around horizontally), you can see the three people in the observation centre above at one point. Look at them closely, because they are fake.
Factual error: During the climax of the film, Flight Director Paul Wick is relieved on the spot for failing to account for weather. In reality, NASA would never simply fire the Flight Director on the spot, but rather declare a "contingency" which puts in place a set of procedures used for emergencies.
Factual error: During the isolation chamber sequence, it is implied that the massive hatch is put in place to prevent exposure to all external stimuli. In reality, there is no "isolation chamber", and the large door is actually the hatch to one of NASA's very large vacuum chambers.
Factual error: During the G-force tolerance sequence, the testing apparatus involves an astronaut sitting in an exposed chair which spins at high speeds. In actuality, an exposed seat would be extremely dangerous for an astronaut, as even a small bit of debris in the air (such as dust, or something falling from the observation platform) could impact an astronaut with extreme force. NASA's real g-force testing apparatus has an encapsulated cockpit.
Deliberate mistake: During the "swirling onion ring" chair sequence, Randall is given a set of goggles that make his eyes "bug out", to enhance the comedic effect of the scene. In reality, these goggles are known as "beer goggles", because they intentionally blur and disorient one's vision. Various aeronautical and military entities use these goggles to simulate less than ideal visual conditions.
Factual error: During the launch sequence, the astronauts are seen moving around in their seats. In actuality, astronauts are strapped in very tightly for launch, as the human body compresses into the seat during liftoff, which might make an astronaut slip and slide around.
Factual error: During the liftoff sequence, an Apollo-style stage separation occurs. This makes no sense, as the spacecraft is a shuttle which doesn't have stages.
Factual error: Immediately before the address to the world, Randall is surprised by unique format of the space toilet. He should not have been surprised by this, as astronauts are trained on the use of space toilets before launch.
Factual error: On NASA's command center monitors throughout the film, the icon used to depict the spacecraft is actually a rendering of the X-33 Space Plane, an experimental spacecraft that was scrapped before the first prototype was ever completed.