In an interview, director Paul W.S. Anderson said that Arnold Schwarzenegger offered to reprise his role as Dutch Schaefer (from Predator (1987)) at the end of this movie as a cameo, but only if he lost the election for California Governor. Schwarzenegger famously won the election, so he was unavailable to appear.
The Antarctic setting on Bouvet Island is based on the unexplained "Vela Incident" of September 22, 1979, where a satellite recorded a flash of light near the island. It was first speculated to have been a man made nuclear explosion, or a natural event, such as a meteor strike, but this has never been resolved.
(at around 1h 6 mins) When Lex asks Sebastian how to say "scared shitless" in Italian, he replies "Non vedo l'ora di uscire da questa piramide con te, perché mi sto cagando addosso." Translated, this literally means "I can't wait to get out of this pyramid with you, because I'm shitting myself."
The Alien Queen was the most sophisticated animatronic ever built at the time. It had twice as many moving parts as the T-rex from Jurassic Park (1993).
(at around 33 mins) The altars where victims were placed in the Chamber of Sacrifices of the pyramid are arranged identically to the hibernation pods in the original Alien (1979).
Tom Woodruff Jr., Alec Gillis: (at around 1 min) After the opening credits are shown, special effects designers as the technicians who discover the heat bloom coming from the pyramid.