Continuity mistake: The view of the front of the moon buggy shows the sunlight coming from the right side of the screen(Pilot's left shoulder) But when we see his view out the window, the sunlight casts shadows as if the sun was behind them.
Factual error: When 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.
Revealing mistake: 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 mistake: 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.
Continuity mistake: The Discovery's crew quarters has five beds, three for the hibernating crew, two for the Bowman and Poole. The exact beds occupied by hibernating crew changes from one scene to the next. This error is caused by Frank's last two running shots (the ones where the camera stayed just ahead or just behind him as he ran) having been accidentally reversed in editting. Frank's hair is parted on the wrong side and the sleep tube layout and the body positions within are precise mirror images of the layout seen in all prior and following shots.
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.
Visible crew/equipment: During one of the scenes where an astronaut does an EVA (Extra Vehicular Activity or "Space Walk"), you see him floating slowly from the Pod shuttle towards the Discovery. This was filmed by hanging the pod on the ceiling and lowering the actor from it with a rope towards the camera that's pointing upward. If you look carefully, you can see the shadow of the rope.
Continuity mistake: When 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 mistake: During the "Dawn of Man" sequence, the ape-man scenes were shot on an indoor stage with projected background images on a huge screen behind the stage. The screen itself was a highly reflective cloth. In most shots, it is quite convincing, but in several (especially when facing the aggressive, victorious group during the first fight, then again when facing the tool-using group in the last fight), the rear screen appears to be a patchwork of smaller pieces of cloth as very obvious puzzle-like shapes of varying reflectivity appear in the sky. Once you notice them, it's incredibly distracting. It was originally parallel strips, but they were VERY visible as vertical lines so they were torn into a patchwork to make lines less obvious.
Continuity mistake: When Floyd and his team are heading to the Lunar excavation site, they start to eat those synthetic sandwiches. One of the shots shows a closeup of Floyd. As he is right about to take a bite, the camera cuts back to a shot of the three men. However, Floyd's sandwich is instantaneously about a foot from his mouth and he is fully chewing.
Continuity mistake: On board the Aries Moon Shuttle is the famous scene when the Pan Am flight attendant serves a meal to Dr. Floyd and then retrieves additional meals, enters the doorway and walks 180 degrees up the wall and over to be upside down to deliver the meals to the shuttle pilots. However, from the outside view of the spacecraft, the pilots are sitting perpendicular to where the passengers sit and she should only have walked up the wall 90 degrees.
Continuity mistake: Frank is running around the centrifuge. He passes the ladder with two bunks to the right and the work station to the left. When Dave comes down the ladder, the bunk is to the left. This error is caused by Frank's last two running shots (the ones where the camera stayed just ahead or just behind him as he ran) having been accidentally reversed in editting. Frank's hair is parted on the wrong side and the sleep tube layout and the body positions within are precise mirror images of the layout seen in all prior and following shots.
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.
Continuity mistake: 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: In the sequence of the shuttle approaching the moon the pilot talks to Dr. Floyd. Floyds food-tray moves away from his knees because of the zero gravity in the shuttle. But it doesn't drift straight away, it swings like a pendulum showing that the tray is hanging on a string.