Continuity mistake: Just before the marines are extracted, Hicks tries to close the APC door. An alien stops the door and tries to get inside. Hicks picks up his shotgun and jams the muzzle into the alien's mouth and fires, killing the alien. The alien falls away, they immediately close the door and the APC begins to back up. The camera shot changes to an outside view of the APC. If you look at the area as the APC backs up, you'll see falling debris but no dead alien. It's doubtful the marines would've pulled it into the APC as we don't see it again, or that they would've kicked the corpse out really far due to the acid.
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: 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)
Continuity mistake: In the original "Alien", Ripley dons a space suit in the shuttle, in preparation to decompressing the quarters to the hard vacuum of space. The helmet has no light on its top. Subsequently, in "Aliens", the opening shots pan through the shuttle chamber, and Ripley's helmet sits there...with a light on its top.
Continuity mistake: In the scene where the drop ship is about to leave the main ship look at the picture on the side of the ship, just to the left of the pilot's window. There is a symbol of an eagle. Note which way it is facing. Later when the ship is on the planets surface and the marines are leaving it, the eagle is facing the other way.
Continuity mistake: When Newt is caged in the resin, the cloud of steam around the egg completely disappears when Newt is seen from the p.o.v. of the egg.
Continuity mistake: Pulse rifles have 10 mm caseless ammo, but if you watch the scene where Vasquez depletes her rifle and then switches to the pistol, there clearly are shell cases being spat out.
Audio problem: In the beginning of the scene where the soldiers are eating in the mess hall, the soundtrack of background noise is played, then repeated.
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)
Visible crew/equipment: When Ripley is first shown in the loader after asking Apone if she can help, after the loaders claws grab the crate and she swings the crate around and asks "where you want it?" you can see tubes trailing off to the left of the loader that don't connect to anything in frame. The tubes are on the right side of the frame just under the crate in the loader's arms.
Continuity mistake: Hicks gives Ripley a wristwatch which is linked to his tracker. If you look at the watch, its face is mostly black with a tiny portion that is clear. However, when Newt has the watch and falls down the tunnel and is wandering around the pool of water before Hicks and Ripley find her, you can see that the watch face has no black - it has a full clear face and appears to be a standard digital watch of the 1980's era.
Continuity mistake: When Ripley is driving the APC, the passenger side front tire is on fire and engulfed in flames. When she runs over the alien with the same tire, the flames are completely gone. In the next shot and several shots after, the tire is completely engulfed in flames again.