Factual error: Although it's already been mentioned that the scene of the shuttle being stolen from the back of the 747 is impossible because the shuttle wouldn't be fueled while being transported, it should also be noted that even if the shuttle was fueled, it would still be just as impossible: During the getaway, the thieves ignited the shuttle's 3 main engines to get free of the 747 and escape: the thing is, the shuttle's main engines are fueled entirely by the large external tank the shuttle and the solid fuel boosters are attached to during liftoff, and once the tank is jettisoned, these engines cannot be used. The only engines the shuttle's internal fuel feeds are the reaction control thrusters, and the Orbital Maneuvering System (which are the two smaller engines located in the bulges just above the main engines). Both the RCS thrusters and OMS engines are almost totally useless within the atmosphere, so even if the thieves managed to get the shuttle free of the 747, they could only get it as far as it would glide unpowered: In fact, they could probably get it farther if it wasn't fueled.
Visible crew/equipment: In the scene where the space station explodes, the wire holding up the model is visible when the explosion backlights it.
Factual error: The space station rotates for pseudo-gravity, but everyone falls along the rotational axis towards the bottom of the screen instead of falling outward from the axis as they actually would. Admittedly this would be difficult to film (Stanley Kubrick's astronaut jogging in a giant hamster-wheel in Space Odyssey - nuff respect) so I guess they just hoped the audience wouldn't know the difference.
Continuity mistake: In the final scene, in the live transmission from the shuttle, there is a full shot of Bond and Holly who are covered by a sheet, and they are at least 4 meters from the camera. In the next shot Bond's face is right in the camera, and he can reach over and turn it off.
Factual error: Two pilot/astronauts steal a space shuttle by firing it up and launching it off the back of the Boeing 747 transporter. This cannot happen : the 747 can't lift the shuttle with a full fuel load - it only just lifts it empty. (Why would they carry a fully fuelled shuttle anyway?)