Other mistake: 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. (00:54:45 - 01:03:15)
Other mistake: Max takes Jinx and puts him in his locker at Space Camp. Wouldn't NASA notice if a $27 million robot went missing?
Suggested correction: I'm sure someone noticed, but the impression is given that a) Jinx is pretty self-automated and b) is considered to be a "bust" of a project (hence the name "jinx"). Most people likely just thought jinx was just wandering around somewhere being annoying to someone else.
Continuity mistake: 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.
Continuity mistake: When Kevin and Kathrine go to the launch pad we see the shuttle on the pad all lit up. When the camera zooms out to show us Kevin and Kathrine in the Jeep, the shuttle is no longer on the launch pad.
Factual error: Mission control begins an auto-landing sequence for the shuttle, but mission control did not have an ability to remote pilot the shuttle when the movie was made and wouldn't get it until 2006.
Other mistake: When they were landing the shuttle, they were able to communicate with NASA in Alabama, but they were in New Mexico. When they were being launched into space, they lost radio contact and the mission control person said 'this bird wasn't flight ready, they only have short range radio'. They were at the most maybe 30 or 40 miles away at the time. So if they could not reach them at that distance, how did the suddenly have the ability to communicate with them when they were over 1,200 miles away? What happened to the short range radio?
Plot hole: In 1986 the only Space Camp was in Huntsville, Alabama. There's no way Kevin and Kathrine drove from Alabama to Florida to see the shuttle on the pad. They couldn't have made the drive in a single night in Kevin's Jeep and be back to Space Camp in the same night.
Factual error: When Control realizes that the kids are communicating with Morse code, they get someone to translate. He reads out "Request alternate landing White" in the space of 9 seconds. The lights and sounds from the CXT switch are not going nearly fast enough for him to have gotten all that. (01:32:20)
Audio problem: When Andi is knocked out by the oxygen tank, Max seems to be yelling as if he's in slow motion, and yet he isn't. Just because he's weightless doesn't mean he can't talk (or yell) normally within his spacesuit.
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 mistake: When the shuttle went into a flat spin, as Katherine is trying to stabilize the ship, the circular motion is forward, but then they show the shuttle spinning side to side.
Plot hole: The whole time they're in space, the main plot is centered around obtaining more oxygen since they only have 12 hours of air but need 14. Time is passing in real-time at a fixed, steady rate based on everything the characters say and do. Yet, every 20 minutes or so, they show the air timer, and suddenly many hours have passed while the characters have accomplished nothing and are still doing the exact same things they were before. It would have made more sense to just say that the oxygen tank only holds 1 hour of air.
Factual error: Before launching, the main engines run for over a minute and a half. That's 20% of the total burn time in a standard shuttle flight, assuming the ET is fully fuelled. There's no way the shuttle would have had enough fuel to make orbit. STS-93 had a very small hydrogen fuel leak in one engine and even then, there was concern that the shuttle wouldn't have sufficient speed for orbit.
Plot hole: The shuttle achieves its accidental orbit, and in need of oxygen they decide to go into a higher orbit to rendezvous with the space station and borrow some tanks stored there. If the shuttle is as ill-prepared for flight as the ground controllers keep saying it is (as it lacks backup oxygen and a communications system), it is highly unlikely the shuttle would have enough fuel to pull off the maneuver to enter a higher orbit (especially given how much fuel was burned off during the test before the accidental launch was triggered). Typically shuttles were launched during specific time frames (launch windows) to enable them to achieve the necessary orbit for their mission directly from launch (such as going to the International Space Station). One of the reasons a damaged Columbia, for example, couldn't unload its astronauts at the ISS was that, aside from not having a docking module, is that it was in a different orbital plane and didn't have the fuel to speed up to the ISS's orbit (which, it is said, would have been roughly equivalent to the fuel needed for takeoff). And even if the orbiter did have enough fuel to pull off the orbit adjustment, it just raises the question of why NASA felt the need to mount the shuttle on two fully operational SRBs and give it all that extra fuel when all they wanted to do was test the orbiter engine (for which empty mockup SRBs would have sufficed if the test really needed to be done on the pad). What is the point of fully mounting a shuttle if it's not for a mission to the point where you don't bother to install life-support or communications?
Factual error: During launch the Shuttle cabin is rather noisy and rattling due to vibrations from the solid rocket boosters and the main engines. After Andie and the Space Camp kids have jettisoned the solid boosters and the external tank, the cabin is still played as noisy and shaky. However, at that point the main engines are shut down and the orbiter is in freefall: there should be no noisy vibration.