Like most films, the movie wasn't shot in sequence. But for added realism, James Cameron filmed the scene where we first meet the Colonial Marines (one of the earliest scenes) last. This was so that the camaraderie of the Marines was realistic because the actors had spent months filming together.
When filming the scene with Newt in the duct, Carrie Henn kept deliberately blowing her scene so she could slide down the vent, which she later called a slide three stories tall. James Cameron finally dissuaded her by saying that if she completed the shot, she could play on it as much as she wanted. She did, and he kept his promise.
Bill Paxton continuously apologized to Carrie Henn throughout filming every time Hudson had to swear in front of her. Carrie later admitted that she didn't mind, mainly because she really didn't know what any of the words meant.
Lance Henriksen had privately pledged to quit acting if this part didn't work out for him after years of journeyman roles. It proved to be one of his most successful films.
Sigourney Weaver's Best Actress Academy Award nomination for this movie was the first ever for an actress in a role in a "sci-fi action" movie (although Jane Alexander had previously been nominated for Best Actress for her role in the apocalyptic drama Testament (1983), and Melinda Dillon was nominated for Best Supporting Actress for her role in Close Encounters of the Third Kind (1977)).
James Cameron: (at around 4 mins) voice over in the opening deep salvage team: "Bio readouts are in the green, looks like she's alive!"
James Cameron: [Biehn's hand] (at around 45 mins) Michael Biehn's character gets bitten on the hand by another character. See The Abyss (1989) and The Terminator (1984).
James Cameron: [strong women] Many of Cameron's films (Piranha II: The Spawning (1982), The Terminator (1984), The Abyss (1989), Terminator 2: Judgment Day (1991), Titanic (1997)) champion strong women, both mentally and physically.
James Cameron: [flying vehicles] The flying vehicles in Cameron's films exhibit helicopter-like flight characteristics regardless of their design. Specifically, the noses of the vehicles dip to initiate forward movement (also: The Terminator (1984), Terminator 2: Judgment Day (1991), True Lies (1994), Avatar (2009)).
James Cameron: [nice cut] (at around 5 mins) a few minutes into the movie, we see Ripley lying in the cryo-tube, and then the scene fades to the picture of the earth; the earth directly fits into the silhouette of Ripley's face.
James Cameron: [feet] When Ripley drives the APC, she crushes an alien's head under one of the wheels.