Plot hole: After the final battle scene we can see Jaws and his blonde girlfriend enjoying a champagne. But they are sitting in a blown-away section of the station which has no gravity.
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.
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 beginnning when Jaws pushes Bond out of the airplane he has a white shirt on. In all the close ups of Jaws he has a tan shirt on. When you see him from far away he has a white shirt on again.
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?)
Visible crew/equipment: In the scene where the space station explodes, the wire holding up the model is visible when the explosion backlights it.
Continuity mistake: When Bond is fighting Jaws while falling from the plane, Bond's chute changes color from a red and yellow pack to a beige and red pack and then back again.
Continuity mistake: In the scene where Bond is in the helicopter being flown from the airport to Drax's estate, both landscape and weather change drastically from one moment to another as he approaches the castle. When the castle is first seen from the air in a long shot, it is surrounded by mountains and the sky is entirely clear. In the shots closer to the castle and from ground level, the mountains have disappeared and there are clouds in the sky. The cloud cover changes as well just after landing.
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.