Numerous differences in the Discovery from 2001: A Space Odyssey (1968), as director Stanley Kubrick deliberately had the models and sets destroyed. Also in 2001: A Space Odyssey (1968), HAL has flat display screens (note the pod bay interface); they are shown here as CRTs.
When Curnow and Max enter the Discovery for the first time, the walls next to the pod bay doors are bare. Later on, the walls have several signs warning that the pod bay must be vented before the doors can open.
As Floyd and Kirbuk have their first conversation, Kirbuk is initially standing with her arms behind her back. As the camera angle changes to face her, her arms are crossed in front of her.
More differences in sets and props from the original film 2001:
After meeting Floyd on the flight deck, Dave moves to starboard, towards the ladder connecting it to the pod bay. In the next scene he is seen entering the storage bay from the far end. In the original film, the storage bay was a dead-end corridor on the port side of the vessel with no connection to the flight deck. Also the chest-pack/suit-thruster controls are considerably smaller than the ones on the suits in the original film.
When the monolith emits the burst of energy towards Earth the pulley link between the Leonov and Discovery One is not visible.
It is stated in the movie that the monolith has dimensions 1-4-9. Its width to height ratio is indeed 4 to 9. However, the thickness is far less than one fourth of the width.
When the crew of the Alexei Leonov reach the Discovery, it is spinning around its midsection (around its port-starboard axis). This is explained as momentum from the rotating crew centrifuge having transferred to the ship over time (the explanation may only be in the novel). The problem is that the plane the Discovery is rotating in is not the same plane as that of the centrifuge - if that momentum had transferred, the ship would be rolling in place (around its fore-aft axis).
When Curnow and Max first reach the Discovery and begin climbing along the spine they walk on the opposite side of the direction of rotation, thus centrifugal force would throw them off instead of holding them to it thus making their climb impossible and not make them feel heavier as they reached the ends.
Jupiter lacks the mass to ignite as a star. In order to even be a red dwarf, it would need around 80 times more mass than it has.
They say the proportions of the monolith are 1:4:9. By direct measurement when the monolith is seen nearly end on, the proportion of thickness to width is about 1:12. The length is unclear as it is only seen at an angle. But if it is 9:4 with the width, the proportions would be 1:12:27.
No pods should be in the pod bay in 2010. 2001: A Space Odyssey (1968) showed 3 pods. All were lost. The first was lost with Poole's body. The second was lost when Bowman blew the exploding bolts to enter the airlock. The third transported Bowman into the worm hole/monolith. When the crew enters the pod bay in 2010, one pod is is still sitting in it's storage area. (Although ignored in the movie, this is explained in the book (section 4, chapter 24). Dave Bowman is supposed to have retrieved pod #3 on remote while preparing his departure.) It is entirely possible that Bowen could have remotely piloted the pod back to the Discovery.
At -100 degrees, one would think there would be no spoiled food odor in the air of the Discovery. The scent molecules could certainly be in the air, and once they came in contact with the human respiratory system they would have thawed enough to be noticed.
Dave Bowman doesn't say "My God, it's full of stars!" in 2001: A Space Odyssey (1968) (though he does say it in the book). However, just because Bowman isn't heard saying it onscreen does necessarily mean he didn't send a transmission with those words.
As Chandra is reactivating HAL, he pushes all but eight bricks in. HAL's voice goes out of control, and Chandra spins around to reset it. When he turns back, there are only four bricks left out of their slots.
When the Leonov crew are attempting to board Discovery, we see that the planet and the moon are being lit from different directions. As they are both being lit by the sun, it's easy to assume they should be lit from the same direction. However, when an observer is outside of, but close to, an umbra of a planet or moon, a crescent closest to the observer will appear to be lit by the Sun. When an observer is close to and between two umbras, which are close to each other, the objects can appear to be lit from different directions.
As the Leonov brakes around the dark side of Jupiter, the cable run used to pull the fireball past the camera is visible. Also, bits of flame can be seen to drop off the fireball as though pulled straight down to the bottom of the frame, when no such thing would happen.
When rebooting the HAL-9000 voice logic circuits, Dr. Chandra's keystrokes do not match what shows up on the screen. He is actually typing the word "continue" when he should be typing "tomorrow" (the word "continue" was already done).
In the first shot of the Leonov, the letters "CCCP" on its hull are backward.
Rope on pulley between ships falls off pulley during a person transfer to Discovery. That would cause the rope pulley transfer to stop, yet it is shown to continue operating.
Rope on pulley between ships falls off pulley during Dr. Chandra's transfer to Discovery. That would cause the rope pulley transfer to stop, yet it is shown to continue operating.
There was no need for Chandra to transfer to the Leonov in such a risky way. There would be plenty of time to transfer after the initial burn and just before the two ships disconnected. They were, after all, going the same speed and essentially motionless in relation to each other.
The joint-mission patch has an upside-down American flag.
During a closeup of a console on the Russian spaceship, a paragraph of instructions written in English for a commercial aircraft lavatory can be seen and read.
If you fail to hear the Russian word for "four" in the countdown spoken by Tanya Kirbuk, the reason is that the word was deleted in versions later than the theatrical release and the early VHS versions because of Helen Mirren's mispronunciation of "chih-TEE-reh" as "chee-TYE-ree".
At the beginning of the film, the graphics showing Dr. Floyd's report of the events in 2001: A Space Odyssey (1968) indicate that the TMA-1 monolith was discovered in the Sea of Tranquility. TMA-1 stood for Tycho Magnetic Anomaly-1 because the monolith was discovered in the crater Tycho. Tycho is several hundred miles southwest of the Sea of Tranquility.
Chandra asks Hal at what rate the number of Jupiter monoliths is increasing, and Hal responds "Once every two minutes." But that's not a full answer without saying WHAT happens once every two minutes. Doubles? That was probably the intent, but maybe it increases 20% every two minutes, or maybe it quadruples every two minutes. Without specifying that, the answer is not an answer at all.
Bowman refers to "The AE-35 antenna." In 2001: A Space Odyssey (1968), AE-35 designated the toaster-sized part in the antenna assembly that Bowman had to replace, hence the reference to a "spare unit." The book further explains that the function of this unit was to control the orientation of the antenna, i.e. keep it pointed at earth. Bowman, of course, knows all this.