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.
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.
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 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.
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 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?)
Continuity mistake: After the elaborate sequence showing each moonraker shuttle docking with the space station, a wide show of the station shows two shuttles frozen in space not attached to anything. The most prominent is the shuttle in the top foreground. The shot looks like a still photo with the exception of the spinning radar dish at the bottom of the station.
Factual error: When a real shuttle is launched (or any other large rocket) the exhaust must be deflected sideways and guided through massive tunnels or trenches so that it does not bounce back into the base of the vehicle and destroy it. The Moonrakers lift off from inside an enclosed structure with no means of guiding the massive exhaust plume safely away. The tiny tunnel through which Bond and Holly escape would have been utterly useless to vent the exhaust of a real shuttle. In common with other movies, the noise and violence of a real launch simply cannot be portrayed accurately.
Continuity mistake: Bond is in his boat being pursued by Jaws in another boat, and as they approach the raging waterfall, Bond activates the emergency hang-glider concealed within the roof of his boat. He flies away and there is no shot of his boat going over the falls, nor is his boat shown still in the water leading up to the falls when Jaws' boat approaches the falls. Jaws and his boat are shown going over the falls, but Bond's boat seems to have simply disappeared. [During filming of the scene Bond's boat got stuck on some rocks and never went over the waterfall as planned. The stuntman doing the handglider stunt would not do it again, so they had to make do with the film they had shot. They only had 3 boats to film the boat chase - one "hero" boat, one to film the hand glider scene, and a empty boat shell to go over the waterfall, which was damaged by the rocks. Still a mistake, but there's why.]
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.
Factual error: Prior to the boat chase, Bond is travelling up river, so he shouldn't wind up at the top of a waterfall.
Plot hole: For the shuttle to land at Drax's Amazon hideout he would need a very long runway, something that could easily be detected by satellite.