Space Camp was filmed at the U.S. Space and Rocket Center in Huntsville, Alabama at the real U.S. Space Camp. The parts in the orbiter were filmed in the Atlantis orbiter used at the camp and the parts in the payload bay were filmed in the payload bay of the Enterprise orbiter that is used by Advanced Space Academy. See more...
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Other: When they first get into space and Tish removes her helmet her left earring is free floating, which would be expected in zero gravity. But after this first shot, her earrings hang down as effected by gravity. Also all three of the girls hair hang down with gravity the whole time they are in space.
Deliberate "mistake": The filmmakers wanted a scene where Andi is startled by Max as he spacewalks behind her at Daedalus. Given that the only way to communicate in spacesuits is through radio, and the two suits would presumably been on the same channel with the shuttle, Andi would have known Max was coming. Further, even if they were on different channels, why wouldn't anyone tell Andi that Max was coming?
Continuity: When Andie goes out to get the oxygen from Daedelus she cannot reach it because her helmet won't let her through the structure of the space station, so Max offers to go and help her because he is smaller, but the only suit they can find is an adult one. After a lot of struggling they manage to make the suit smaller and he fits through the structure to get the oxygen but his helmet is the same size as Andie's so although his suit was smaller, he should not have been able to fit. Also notice how long her belt is when Max emerges from the ship. She would have to have about 30 ft of belt to wrap that much around him.