Continuity mistake: When the search party goes into the boneship, they are wearing full space suits, and hoods under their helmets. When Kane's helmet is first cut off, he has no hood on. (00:36:45)
Visible crew/equipment: When Ripley is heading towards the Shuttle towards the end, just before she finds Jonesy, there is a POV shot where the camera is walking towards a ladder. If you look at the floor you can see the dolly that the camera moves on. (01:36:05)
Continuity mistake: While Parker is decapitating Ash with the fire extinguisher his T-shirt is not torn, just after he says "Ash is a goddamn robot" his T-shirt is now torn and held together with a safety pin. (01:23:20)
Continuity mistake: When the crew is chiding Parker for Brett saying nothing but 'Right' all the time, Brett's cigarette is first short, then long, then short again.
Visible crew/equipment: When Kane is struggling on the table shortly before the alien rips through his chest, just before the first patch of blood appears, his T-shirt rides up and something strapped to his chest can be seen. This is some sort of pack containing fake blood that discharges onto his T-shirt. (Best viewed in slow motion.) (00:55:40)
Continuity mistake: When Lambert deactivates Ash by using a cattleprod, you will notice that she is wearing brown cowboy boots. Minutes later as the Alien goes to wrap its tail round the back of her legs, she is now wearing a sneaker - though you only see the toe cap it is clearly not a brown cowboy boot. (01:23:55 - 01:33:40)
Character mistake: When Ripley is talking to "mother" by typing, it types "Emergency command overide 100375". "Override" should be spelt with two R's. (01:19:34)
Revealing mistake: Parker had hair. When the alien bit through his head the melon they used did not have hair. Also, the seeds can be seen inside the melon when paused at the right moment. (01:33:35)
Revealing mistake: When Parker shoots the blowtorch at Ash, Ash's face begins to melt off. When the skin melts off we see, in slo mo, that the dummy they used has a sealed mouth. (01:27:25)
Continuity mistake: Near the start, when Dallas is at the entrance to Mother, one of the lights to his left, the fifth one down from the ceiling, is not lit. The next shot from inside Mother looking out shows that light is now lit. This exact same thing happens a second time when Ripley is entering mother later in the movie. These two scenes must have been shot at the same time. (00:08:20 - 01:18:35)
Suggested correction: That light totally had enough time to light between the frames, because it was hidden by the sliding door for a brief moment. Lights were lit one at the time, not all at once, so this one starts to shine just a little bit later than all the others, that's it.
I consider this a valid mistake and the correction is a stretch. The lights only took about 2 seconds to light up, but she's at the door for almost 3.5 seconds after they're on and the last light did nothing. Then in the half second it took the door to open, the last light is now on.