It was conceptual artist Ron Cobb who came up with the idea that the Alien should bleed acid. This came about when Dan O'Bannon ran into a wall with the screenplay in how to handle the last half of the movie. He needed a good reason for why the crew members don't just shoot the thing and kill it but still not make it an indestructible monster that can't be killed. The acid blood was the idea that solved this problem.
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.