The futuristic computer that Roy Scheider is using on the beach planning for the mission is an Apple IIc with an LCD screen. The Apple IIc was a full-strength Apple computer with 128k of memory, two serial ports and a mouse in an 11in by 12in box small enough to fit in a briefcase. Impressive stuff at the time.
(at around 21 mins) When Dr. Heywood Floyd stands in the doorway of his sleeping son's room, on the wall to the left of his bed is a poster of an Olympic runner with the text "Beijing 08" on the bottom. Considering the film was made in 1984, and the Olympic Committee did not chose Beijing for the Olympics until July 2001 is a fun example of life imitating art and background detail that came true.
The phrase "My God, it's full of stars" was not a part of the film 2001, but was a part of the novel. In the novel, the "star gate" monolith was found on the surface of Saturn's moon Japetus (or Iapetus), rather than floating in space near Jupiter. As Bowman flies over the monolith, it suddenly changes from a towering slab to an infinite tunnel. As this happens, he utters the final phrase: "The thing's hollow! It goes on forever, and... oh My God, it's full of stars!"
During the planning stage of 2010 (1984), an email connection was provided for Peter Hyams (in Hollywood) and Arthur C. Clarke (in Colombo, Sri Lanka) so that Hyams could regularly consult with Clarke about how to adapt the novel to the movie screen. In 1983/4, such an email correspondence was practically unheard of outside the academic community, and it was certainly the first for the film world. Edited highlights of the emails were published as a book, "The Odyssey File", in 1984.
The blue spacesuit on the Discovery (the only one that was never used, in either 2001: A Space Odyssey (1968) or 2010 (1984)) was later used in the Babylon 5 (1994) episodes #1.20, "Babylon Squared" and #3.17, "War Without End: Part 2"
In 2001: A Space Odyssey (1968), HAL tells Dave that his teacher was Mr. Langley. In this film, we are told that Dr. Chandra (Bob Balaban) was his teacher. This is actually not a continuity error. The novelization of 2001 identifies Dr. Chandra as HAL's teacher, but Stanley Kubrick changed that name for the film. Peter Hyams may not have known this, as he didn't make the corresponding change for this film. Mr. Langley and Dr. Chandra are really meant to be the same character.
EASTER EGG: On the Leonov miniature: to the lower right of the "LEONOV" marking on the starboard side of the ship is a tiny decal reading "SDELANO V SShA", meaning "Made in USA". It is barely visible on the Blu-Ray in the shot where Brailovsky and Curnow exit the airlock.
The voice of the SAL 9000 computer was actually performed by Candice Bergen, though the role was credited to "Olga Mallsnerd," a pseudonym combining the surname of Bergen's spouse (director Louis Malle) and that of Mortimer Snerd, one of her father (ventriloquist Edgar Bergen)'s famous puppet characters.
Some of the products, organizations, and locations in the film no longer exist at the time of the film's events. For example, as of the events of 2001: A Space Odyssey (1968) (let alone 2010 (1984)) Pan Am Airlines had gone out of business. The Soviet Union, and along with it, the Soviet Air Force, of which Kirbuk was a member, and the Communist version of Pravda magazine had all ceased to exist by 1991. Also, by 2008, The Houston Astrodome and the original Yankee Stadium, both referenced for their stadium hot dogs, no longer hosted sporting events.
The score was originally composed by Tony Banks (of Genesis), but Banks' score was ultimately dropped. David Shire was brought on board to do the final score for the film. Tony Banks later used parts of his score for the film Lorca and the Outlaws (1984), and was released on his 'Soundtracks' album.
The blue spacesuit, a holdover from 2001: A Space Odyssey (1968), is missing its helmet, apparently because the producers thought that Dave used that helmet while trying to disable HAL in the original film. But Dave actually used a green helmet - part of a green spacesuit which was stowed in the emergency airlock.
Victor Milson states that a U.S. Navy vessel called "U.S.S. Cunningham" participates in a deadly naval engagement with a Russian vessel. Given the film was made less than 10 years following the end of the Vietnam War, it could be held, that a futuristic Navy ship named "Cunningham" may have been named after U.S. Navy Commander Randy "Duke" Cunningham, who, at the time, was a notable, decorated Vietnam War hero. However, Cunningham will be best remembered by the public as a disgraced United States Congressman.
When director Stanley Kubrick was not interested in creating a sequel to his own 2001: A Space Odyssey (1968), director Peter Hyams showed interest. He contacted both writer Arthur C. Clarke and Kubrick for their approval. Kubrick assured him he was fine with it, and encouraged Hyams to make the movie he wanted to.
The nurse at the home where Bowman's mother is staying is reading a Time magazine with a cover story about the impending war between the US and the Soviet Union. The leaders on that cover are stylized depictions of Arthur C. Clarke and Stanley Kubrick.
The set for Heywood Floyd's house (with dolphin pool) was constructed atop the MGM studio "saucer tank" in Culver City, California. The dolphins, named Captain Crunch and Lelani, were provided by a local aquarium.
The pod that Max takes for his ride to the Monolith has a Russian word "GRAMPI" written on it. This word is a Russian transliteration of the English word "GRUMPY". In Russian the correct word would be "SERDITY". (However, the character of Grumpy in the Russian translation of Snow White and the Seven Dwarfs (1937) was named "BORCHUN").
In the first shot of the Leonov's interior, the camera opens on a closeup of a computer monitor in sickbay. Below the monitor is a decal with several lines of English text, which were part of the zero-gravity toilet instructions from 2001: A Space Odyssey (1968).
The monitor box that's on top of SAL 9000 early in the movie is shaped exactly like the Kaypro portable computer that Arthur C. Clarke used to communicate via email with Peter Hyams during the movie's production. Later, when Dr. Chandra is inputting commands to HAL 9000 in Discovery, initializing his voice recognition capability, the keyboard he is typing on is from a Kaypro portable computer.
During the conversation between Floyd with Moisevitch (Dana Elcar) Floyd mentions wrongly the spaceship Titov, renamed as Aleksei Leonov "because the other name wasn't so popular", in Moisevitch's words. German Titov was a Russian cosmonaut who traveled in the spacecraft Vostok 2 in 1961, giving a complete turn around the Earth.
The anti-nuclear sign visible in wide-screen when Arthur C. Clarke makes his cameo in front of the White House, was an actual long-standing icon in Lafayette Park on the far side of the executive mansion, tended for years by an activist, and which grew in size by degrees over several years. The depicted version was an intermediate one. An even larger version would be banished when all semi-permanent protest displays were banned from the park due to increased security concerns.
The Russian space station Sergei Kirov (which is mentioned as having destroyed an American satellite) was named for an early Bolshevik leader, one of the first to be killed in Joseph Stalin's "Great Purges".
The trivia items below may give away important plot points.
In the original novel book the final message that HAL 9000 sends to planet Earth is "All these worlds are yours except Europa. Attempt no landing there". Hyams added two lines for the movie, "Use them together. Use them in peace", to give it more transcendence to the message in its sending to human race.
At the end of the movie Jupiter explodes by effect of millions of monolith aliens, turning it in a new sun. In the original book this sun is called Lucifer, a play-on-words of Jupiter (same vowels in the same place, but turning a few consonants).
During the conversation between Floyd with the Leonov's crew, it's mentioned that the monoliths be proportional to 1x4x9, squares of 1x2x3 respectively, and that these proportions are perfect even using a six decimal table. 1x4x9 is a symbolism of the three space dimensions (width, length and height) to indicate monolith's divinity.