Factual error: In the scene in which we see the space station from the cockpit of the approaching shuttle, the station does not appear to rotate because the shuttle is rotating at the same speed. OK...except that the station IS still rotating with respect to the sun, which means that the light source and shadows on the station should be moving.
2001: A Space Odyssey (1968) - 29 mistakes
Directed by Stanley Kubrick, starring Gary Lockwood (add more)
Continuity: In the scene where the astronauts are approaching the monolith on the moon, the earth is clearly seen in a gibbous phase near the horizon. In the next scene, the sun passes behind the earth, which is now in a "new" phase overhead. The earth does not change its position in the lunar sky, and certainly cannot change phase that fast.
Revealing: When the astronauts are on the way to the monolith on the Moon, there are two windows seen within the interior of the small space shuttle. During their small lunch, in the left window, the horizon is seen as the surface of the Moon is flowing back against the direction of the flight. However, although sometimes this horizon fills up to half of the window, no horizon can be seen in the right window despite being located directly beside the left window. Nevertheless, the inclination of the Lunar surface should allow for it to be seen.
Continuity: When Frank receives his parents' birthday message he is relaxing on the sun-bed. As the message drags on there is some intercutting with various other views about the room. One shot happens to be of the sun-bed from an alternative angle, and Frank is nowhere to be seen. In the next shot Frank is once again lying on the bed.
Factual error: On board spaceship Discovery, the crew's living area is the spinning centrifuge, which spins about its axis to generate a gravity-like acceleration at its perimeter, the floor. When exiting the centrifuge a crewman climbs a ladder from the floor up to the hub, where there's a door leading to other parts. When Poole & Bowman climb this ladder, it's evident that they're under full body weight the whole way up. But in reality they'd get steadily lighter toward the hub. In fact, they'd be practically weightless within a few feet of it.
Continuity: For most of the sequence during which the Orion space shuttle closes in to dock with Space Station One, we see the space station rotating counterclockwise, as viewed from the side the Orion is approaching. But the first two times we see the station (immediately before and immediately after the scene in which Floyd's pen floats free aboard the Orion), it is rotating clockwise. It is also apparently rotating clockwise in the shot from inside the station, looking out at the approaching Orion. The stars in this shot are turning clockwise, implying that the station is moving anti-clockwise, hence must be rotating clockwise when observed from the Orion.
Factual error: During the base briefing all the participants are walking quickly as they would on Earth. This kind of motion is impossible in the lower moon gravity and it is made clear throughout the film that no artificial gravity technology exists that might allow Earth-normal movement. Later, at the monolith excavation site, the walking is slower and more deliberate as it should be.
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