Shared with you
After the crew awakens from hypersleep, the navigator Lambert announces that the ship is "just short of Zeta 2 Reticuli." Zeta Reticuli is a real double-star system about thirty-nine light-years from Earth, and has figured prominently in U.F.O. lore. In the 1960s, Barney and Betty Hill claimed to have been abducted by "gray" aliens from Zeta Reticuli.
The blue laser lights that were used in the alien ship's egg chamber were borrowed from The Who. The band was testing out the lasers for their stage show in the soundstage next door.
The chestbursting scene was NOT filmed in one take (despite the myth). The scene was filmed twice: on the first take, the chestburster was unable to cut through Kane's shirt, so the crew needed to reset and shoot it again. The failed attempt is visible in the finished film, since director Ridley Scott thought it made it look like the creature was struggling to push its way out, and made the scene more violent (see The Beast Within documentary where this is discussed). According to designer Ron Cobb, the two takes of the scene were shot from multiple angles, and about 40 minutes of footage was available for screening.
Shredded condoms were used to create tendons of the beast's ferocious jaws.
According to Yaphet Kotto, Sir Ridley Scott told him to annoy Sigourney Weaver off-camera, so that there would be genuine tension between their characters. Kotto regretted this, because he really liked Weaver.
To get Jones the cat to react fearfully to the descending Alien, a German Shepherd was placed in front of him with a screen between the two, so the cat wouldn't see it at first. The screen was then suddenly removed to make Jones stop advancing and start hissing.