Shared with you
Brett's death was storyboarded by Sir Ridley Scott originally for the Alien to use its inner mouth to take his heart out of his chest, harkening back to the image of the space jockey. The Alien would then leave Brett, where he would be found by Parker and Ripley, who'd cradle his body. Scott abandoned this idea, due to it being too similar a death to the chestburster scene, and the scene that now plays, was made up on the day it was shot. In the scene as filmed, the Alien would grab Brett's head so tightly in its hands that blood started pouring from it as he screams for Parker and Ripley. However, the studio balked at the amount of blood, so in the finished scene, there is only a brief shot of the Alien breaking Brett's skull with its jaw, and pushing him to the ground before it drags him up towards the air duct with the cat watching. The Director's cut restores a shot where Parker and Ripley come in and see Brett being dragged off for a brief moment.
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 did not make it through Kane's shirt, so the crew needed to reset and shoot it again. The failed attempt is visible in the finished film since Ridley 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).
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.