Continuity mistake: During the alien chest-burster/death of Kane sequence, Kane's shirt switches back and forth from being tucked-in, to being un-tucked throughout the scene.
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.
Visible crew/equipment: After Ripley fails to shut off the auto destruct sequence, she runs through a corridor filled with gas. As she exits from the gas right before the shot cuts away we see her pass by a full sized light. Beside this light is the clear arm and head of a lighting crew member. (This is acknowledged on the DVD commentary).
Continuity mistake: When Ash has gone crazy and is attacking Ripley, his white android juice/sweat/fluid is flowing from his forehead. After he throws Ripley into the room with the nude pictures on the wall, there is a new shot. In it, Ash is walking into the room, but there is no android fluid on his forehead.
Continuity mistake: In regards to the self destruct mechanisim of the Nostromo, It is said that the time from the setting to detonation will be 10 minutes. This is also confirmed by the voice of "Mother" who says, right after Ripley initiates the sequence, that the detonation will take place in "T-Minus 10 minutes" However, in the next shot you see one of the monitors which shows a countdown with 10 minutes and an extra 30+ seconds on it.
Continuity mistake: In the shot of the alien's tail wrapping around the back of Lambert's legs right before it kills her, the floor is different to what it was before, there is water suddenly falling from the ceiling when there wasn't before and her trousers have changed from white to blue. This is because that shot was originally intended to be used when Brett was killed.
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.)
Plot hole: When Ripley goes to access the computer Mother, the entry door opens and closes with a hissing noise, a couple of minutes later you see Ash next to Ripley with a smile on his face. How did Ash manage to open the same door without it making the hissing sound? Ash could not have been in the room before Ripley came in - once Ripley has sat down at the console, it rotates on a 90 degree angle, this would have made it impossible for Ash to be hiding behind a desk or a computer console without being seen by Ripley. There are many doors on the ship that make the same hissing sound when the doors open, an obvious example is the infirmary door. And Ash couldn't have disabled the pneumatics of the door, because when Ripley exits the room, the hissing noise is heard again.
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.