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 scene, 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. Henn later admitted that she didn't mind, mainly because she really didn't know what any of the words meant. Years later, during cast reunions, Henn had grown up so much that Paxton didn't recognize her at first.
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 had several notes for James Cameron after having read his script, which were mostly about how she felt Ripley should respond to her situations, which he was happy to accommodate. Cameron praised her for never taking issue with the direction he wanted to take with the story, even with the points they couldn't agree on. One of them was the amount of gun violence; Weaver had initially focused on the script's dialogue rather than stage directions, so when she arrived on set, she told Cameron that as an advocate for gun control, she was uncomfortable with all the shooting. Cameron felt that this was perfect for Ripley, who is equally reluctant to use a gun unless forced to, and told Weaver to bring that attitude to her performance. He also took her to a gun range to try and fire an automatic gun, which she had to admit was pretty cool.
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: [feet] (at around 1h 7 mins) When Ripley drives the APC, she crushes an alien's head under one of the wheels.