Factual error: While the Leonov has a centrifugal section to simulate gravity, the ship's bridge is not part of it (evidenced by the stationary views outside its portholes). Yet in various scenes, including the one when Floyd rushes in to discuss his plan to return to Earth sooner with Tanya, gravity seems quite evident. Floyd marches across the compartment onto the raised pilot area's floor, then steps down from it, his foot landing audibly. Tanya's open jacket also hangs down normally as she moves about. Yet when Floyd demonstrates his plan using two pens, they float in mid air. (01:26:50)
Factual error: In the scene where the crew members are doing a simultaneous countdown in Russian and in English, the Russian crewmember skips the number four (chetiri). She goes straight from 5 (pyat) to three (tree). (01:44:14)
Other mistake: After speaking with Dave Bowman on her TV, Betty lays her head on the table and we see an obvious cut & paste as her form shifts slightly. (01:09:35)
Continuity mistake: Toward the end of the chat in front of the white house, in a far shot, Dr Floyd crosses his legs. The camera comes in for a close-up and he crosses his legs again. (00:11:52)
Factual error: In the vast majority of cases, U.S. Astronauts wear the US flag on their left arm. On the rare occasion the flag is on their right arm, the flag is reversed so that the blue field remains toward the front of the person wearing it. The patch on Dr. Chandra's space suit during the launch countdown to leave Jupiter is on his right sleeve but is a left-sleeve patch. (01:37:00)
Continuity mistake: During the "aero-braking" maneuver the force dislodges a photo from Dr. Floyd's wall and stretches his face indicating many Gs. Similarly, the cockpit crew is thrown back into their seats, yet their flimsy microphone headsets are never dislodged from their heads. (00:35:22)
Factual error: The filmmakers here forgot how a centrifuge works to mimic the effects of gravity. It is centripetal force wherein an object is pulled away from the center of rotation (you feel its effect on a merry-go-round when it spins really fast and you are tossed off by the centripetal forces). No gravity is actually created. So when the two astronauts are walking along the outside of Discovery and Curnow announces he is getting heavier, it is impossible. First, he's not within Discovery (and if he were, the force would pull him toward the ends of the ship - correctly depicted later when the men are shown walking on the inside of the pod bay doors). The area they are walking on is dropping away from their feet. Both men should be motionless in space as the ship falls away 'below' their feet, then rotates around and kills them when it clobbers their heads half a rotation later. (00:47:50)
Continuity mistake: At one point when Chadra is repairing HAL, HAL starts speaking gibberish. When HAL starts doing this there are 8 blocks sticking out from the floor, but when Chandra stops HAL there are only 4 left. (00:55:15)
Continuity mistake: When Dr. Chandra enters his office he throws his keys onto a stack of papers on his desk. In subsequent shots, the keys are missing or appearing again. (00:13:45 - 00:15:20)
Continuity mistake: Near the end, the Discovery's antenna is shown in a closed position (not pointing anywhere) before it moves, meaning prior to this scene, it could not have been used to communicate with the Leonov.
Continuity mistake: In "2001", Bowman sneaks aboard Discovery through the emergency airlock. In the airlock's alcove is a spare spacesuit, green in color. He takes and uses the green helmet to cross the decompressed pod bay to access HAL's memory. After disabling HAL, Dave wore his red suit and helmet to leave Discovery for the last time, and would have had no reason to move the green suit before leaving, and no one else is aboard to have done so. In this film, we see the same alcove is entirely empty - the green suit has vanished. (01:41:50)
Continuity mistake: When doctors are discussing the medical condition of Dave Bowman's mother, a close-up of the African-American doctor shows a framed newspaper on the wall behind him. It is the front page and has prominent pictures of Bowman and Poole taken during their mission. In the next, wider shot, we see this wall suddenly has nothing on it - the newspaper and frame have vanished. They return when Bowman's mother sits up in bed. (01:16:45)
Revealing mistake: When the Russian pod is launched, a wide shot shows the Monolith at top/right with Jupiter in the background and both the Leonov and Discovery at bottom/right with the pod nearby. Just before this shot ends, all three spacecraft vanish, leaving only Jupiter and the Monolith for a very short but obvious moment. (01:04:35)
Continuity mistake: Dr. Chandra is in the logic circuits room reactivating HAL. He types words into a computer on the wall opposite the logic circuit panel (panel with the clear plexiglass blocks). In the movie 2001 there was no computer screen there; when Bowman is deactivating HAL you can see the flat metal wall with the red grid on the wall opposite the logic circuits. (00:55:50 - 01:34:05)
Plot hole: When the doctors are discussing the condition of Bowman's mother, a newspaper headline on the wall displays the pictures of both Bowman and Frank Poole. These pictures are actually still shots of the two actors from an earlier conversation they had with HAL in the previous film. Since Discovery has been dormant for nine years, how did Earth manage to use these particular shots for the newspaper?
Deliberate mistake: Dr. Chandra returns to the Leonov at the end of the film with the device that Dr. Floyd designed to cut HAL's memory circuits. He hands the device back to Dr. Floyd, who tosses it in the air and catches it when it falls back into his hand. One problem - there was no gravity on the ship at the time. (01:44:00)