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.
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.
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?
Answer: Not necessarily. The 3 G's pretty well kept her pinned, so she wasn't bouncing around. If someone can fall 18,000 ft out of an airplane with only a sprained leg (one of several examples) then yes it's theoretically possible. If the guy in this story could withstand 42 g's strapped in, the yes Katherine could've survived 3 g's.
Https://www.pbs.org/wgbh/nova/article/gravity-forces/.