Continuity mistake: Right after Ripley is rescued from the Narcissus, look at her hair in the clinic. At first there is a wide angle shot of the nurse coming over to her with some small talk. Then, when the shot changes to a close up of Ripley and the nurse, her hair has puffed out about 2 inches more. (00:05:40)
Continuity mistake: When Gorman and Burke come to see Ripley to persuade her to come to LV-426, Burke hands her a plastic card so she can call him if she changes her mind. At this point Ripley lights a cigarette. The scene then cuts to a view of the whole room, and Ripley can be seen lighting the cigarette again. (00:15:15)
Continuity mistake: From Director's Cut. The scene where Al is being quizzed about the ownership of the discovery of the object discovered by the "Mom and Pop" survey team tells us that a call has been put in by that team to the base. But then when they discover the ship, where is the call? They explicitly do not call it in. Now this is not just a general enquiry because they were sent out there two weeks ago to a specific grid reference. "He says he's onto something." (00:16:34 - 00:18:38)
Revealing mistake: When Bishop is doing his knife trick on Hudson it's obviously fast forwarded as you can clearly see the head of Apone in the background move way too fast for real life. No one can move their head that fast without snapping their neck. (00:21:25)
Continuity mistake: Director's Cut: During the briefing scene on board of the Sulaco, Lt. Gorman begins the briefing. He gets interrupted by Hudson. Before the shot changes to Hudson, you can see Gorman standing straight in front of the marines and looking straight ahead. In the shot from Hudson, you can see Gorman looking to the right to face Hudson. He still should be looking straight ahead. (00:32:00)
Continuity mistake: When Ripley is giving Newt the cup of hot chocolate the handle is on Newt's right. When it shows the close up shots, the handle is on Newt's left. (00:48:40)
Continuity mistake: When the Marines first enter the reactor room, the "Mission Time" readout on the shoulder mounted cameras jumps backwards and forwards in time with every cut. (00:54:10)
Continuity mistake: When the marines first encounter the Alien hive in the reactor, and Ghorman asks Hudson what he's seeing, we're treated to a shot of Vasquez' helmet cam, and her name in the bottom right is missing her first initial. [Timecodes are from the special edition of the movie. The first one is the one for the error, and the second is a different scene with the initial present for comparison.] (01:04:00 - 01:20:00)
Continuity mistake: In the sequence when the APC is fleeing the hive, and the alien punches a hole through the windshield to get to Ripley. The hole disappears in the next shot when the light reflects off of the glass. (01:07:05)
Visible crew/equipment: In the Reactor Room scene, where the Marines first encounter the aliens, there's a part where Dietrich is grabbed from behind and accidentally ignites Frost with her flamethrower, causing him to fall down the stairwell. As he's falling, if you look, you can see part of a leg and a cable belonging to one of the technicians on the set. (01:14:05)
Continuity mistake: In the APC, Ripley puts on a headset to talk to Hudson. When the fighting is underway, she turns to Gorman to "get them out of there." Headset's gone. Next cut to, headset's back for Gordan to pull it off of her. (01:15:30)
Other mistake: When the autoguns fire at the aliens for the second time, there is a flashcut of an alien being blasted apart. Watch closely; it's the same clip of the alien that Vasquez shot and subsequently sprayed Drake with acid. (01:18:00)
Continuity mistake: In the shot were Ripley is driving the crew away from the aliens, note the big dent in the vehicle. Then in another shot when they finally get outside, there's a shot from the side and the dent is gone. (01:19:15)
Continuity mistake: During the scene where Ripley is trying to break the window with a chair, there is a scuff mark on it before she hits it. It goes away and comes back. (01:32:15)
Suggested correction: The view from Ripley's side is looking up at the window and from the other side level where there are reflections at the same height (using Ripley as a reference) of the scuffs. There is no way to tell if the scuffs are there or not.
The Director's Cut (and maybe even on the theatrical version) on the 2010 Blu-ray removes the scratches, so I assume they were not supposed to be there initially.
Continuity mistake: Towards the end of the film where Ripley and Bishop are in the dropship flying towards the atmosphere processors, Ripley begins to build a composite weapon from a flamethrower and a pulse rifle. She pulls a flamethrower from a rack on the wall, but lays pulse rifle on the deck of the ship, and then pulls a pulse rifle from the rack and lays a flamethrower on top of the pulse rifle. (01:49:05)
Revealing mistake: When Ripley rescues Newt, an alien comes from a corner and it jumps from side to side. In the second jump, you can see two wires on its back. (01:50:30)
Continuity mistake: You may need slo-mo to see this: towards the end of the film, when Ripley is going down in the elevator to save Newt, pay close attention to the indicator screen counting off the floor numbers as they pass by. It goes floor 8, 7, 6 then 7 again and then 5. (01:51:20)
Continuity mistake: When Ripley enters the hive, right before she lights the second flare, she fires a flamethrower burst. When she does, the starter flame goes out, then in the next scene it is on again. (01:53:50)
Continuity mistake: In the end of the film, when Ripley pulls the Alien queen down in to the hatch we can see that the bulb on top of the machine cracks but when they are lying on the hatch the bulb is whole. (02:05:10)
Continuity mistake: When Ripley and the Queen fall into the airlock, look closely at the Queen's tail. It seems that the sharp end of it is broken off, or missing. Later on in that scene it is back. (02:10:25 - 02:11:25)