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)
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.
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.