"I'm sorry, Dave. I'm afraid I can't let you do that."
"My god, it's full of stars!" — This line appears in 2001 the book, but not in the movie. Nevertheless, in 2010the movie, it's claimed Bowman said this before entering the Star Gate.
Any time jaunty classical music is used in a space setting, particularly Johann Strauss Jr.'s Blue Danube waltz.
Cast the Expert: After failing to find a British actor who could play the Mission Control CapCom, Kubrick hired a real U.S. Air Force air traffic controller stationed in Britain. The interviewer from the BBC was also played by a real BBC newsreader.
Doing It for the Art: Stanley Kubrick and Arthur C. Clarke spent enormous efforts into making everything as realistic as possible. The earth-moving equipment seen on the Moon would actually work on the real Moon. Quite a few experts from NASA and IBM were asked to help design the sets.
Clarke published a few lines from his diary from pre-production in the introduction of a re-issue of the novel. They include "rang Isaac Asimov to ask him about the biochemistry of turning herbivores into carnivores." (Asimov, besides writing science fiction, was a professor of biochemistry.) And they never even did anything with that...
Rather than using bluescreen, Kubrick filmed all the model shots against black backgrounds and required the compositing work to be done by a team of British animators painting traveling mattes by hand frame-by-frame to mask out each element. When production ended, most of the animators signed onto Yellow Submarine in order to work on something colorful after spending two years painting little black blobs.
Instead of storyboarding the docking sequence, multiple model sequences were shot so Kubrick could edit them down.
Fake Russian: Brit Leonard Rossiter as Dr. Smyslov, the guy who grills Floyd about just what's going on at Clavius.
Flip Flop of God: What exactly the orbital platforms are for. Originally they were intended to be nuclear delivery systems, but this was later retconned to leave their purpose ambiguous.
Prop Recycling: Deliberately averted. Kubrick had all the sets, special effects models, and design notes destroyed after filming was complete, to prevent them being reused in low-budget B-movies. The production crew for 2010 had to rebuild everything by examining the film itself, frame-by-frame. A deliberate case of No Plans, No Prototype, No Backup.
It didn't work. Several models (rebuilt or maybe the same film clip) have been used. Space: 1999 used the same rocket landing site on the Moon.
Life Imitates Art: In spite of the long Science Marches On listing below this, the movie features a brief sequence wherein HAL and Dave play chess together. This was years before computers were designed with the ability to play chess, and then later stacked up against Grandmasters.
Besides technology progressing slower than the production team anticipated, there are two details of astronomy in this movie that have since become dated. Kubrick insisted that the artists paint the Earth very pale blue because its albedo is 0.38. Only a few years later, photos from the Apollo missions made everybody realize that this figure is averaged over the pure white clouds and the deep blue oceans. Jupiter and its moons were also intentionally depicted vaguely because of the limitations of ground-based telescopes.
The film's depiction of the lunar landscape owes much to the craggy, mountainous terrain that was common in science fiction before the Apollo landings. Nonetheless the film is surprisingly accurate given that the production predated even the Surveyor probes, let alone manned exploration.
Floyd and everyone else on the Moon walk around completely normally. The Apollo landings later revealed that a loping gait was required in the Moon's 1/6 gravity.
The proto-hominids in the opening sequence are all about the same size, but current theories and fossil evidence suggest that the males should've been substantially larger than the females.
The notion that the Monolith's influence guided one of the hominids to pick up a bone and start hitting stuff with it loses much of its impact, now that it's known that tool use also occurs in our great ape cousins, as well as ravens, monkeys, elephants, dolphins, and dozens of other genera that aren't our close relatives. The scene still works as a metaphor, but in the literal sense, those creatures should've come up with tools as basic as clubs long before they left the trees.
Shrug of God: Certain ambiguous or unrealistic elements have been shrugged off by Kubrick and Clarke, such as the true meaning of the Monolith or how HAL was able to read lips from the side. The latter has since been vindicated in recent years. Computer techniques have been capable of figuring out words from using a side camera view for quite some time now.
What Could Have Been: Kubrick had allegedly asked Osamu Tezuka to work as a production designer for the film, but sadly, The God of Manga was far too busy with his own projects to oblige.
Also worthy of note is that Kubrick approached the rock group Pink Floyd to do the music to the film (as well as the later Clockwork Orange), but they declined. Roger Waters later said not scoring 2001 was one of his biggest regrets. (Supposedly "Echoes" syncs up to the third act of 2001, try it out.)
In turn Waters asked Kubrick for permission to use a sample of the "My mind's going, Dave" dialogue on the beginning of the track "Perfect Sense (Part I) on Waters' 1992 solo album, Amused To Deathnote Roger meant to use it as a Take That to ex-bandmate-turned-bandleader David Gilmour, with whom he was feuding five years previous for the rights to the Pink Floyd name; Kubrick refused to let him. Waters instead left a backwards Take That to Kubrick in place of where the ''2001'' dialogue was to be on the album.
Hal is activated on January 12, 1992. The day, now passed, was not particularly notable.
Notable, but not plot-relevant. The scene with the primates is obviously not 2001, but the title card for the Discovery mentions that it is 18 months later. This places the trip to the moon (and discovery of the monolith) in 1999.
Some say the discovery of the monolith happened in 2001, which sets up the odyssey.