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When Rodney goes back to check on the nukes for the first time, he mentions that there are two "TK421" bombs and a "1138". TK421 was the stormtrooper number Han Solo used in Star Wars: Episode IV - A New Hope (1977) as well as the stereo system mentioned by Buck in _Boogie Nights(1997), and 1138 is a reference to THX 1138 (1971), an early George Lucas film.
The display used when Sam, inside the drilling machine, is monitoring the materials in rocks that they are about to drill through, is reused in Epoch: Evolution (2003). Before the "object" in that movie is unlocked and entered, one of the displays used to monitor technical data is exactly the same display used in "Deep Core".
Bruce McGill's character's surname "Dalton" is most likely a reference to his reoccurring character on the series MacGyver (1985), Jack Dalton.
The cello concerto written for this film by Erich Wolfgang Korngold was composed as two shorter pieces for filming purposes. After the film was released, they were combined as two movements of a finished concerto, making Korngold's "Cello Concerto" one of the shortest on the concert hall stage, at about 12 minutes.
