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.
Continuity mistake: During the alien chestburster/death of Kane sequence, Kane's shirt switches back and forth from being tucked-in, to being un-tucked throughout the scene. (00:56:15)
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)
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. (01:35:55)
Continuity mistake: When Dallas, Lambert and Kane first discover the Space Jockey, the room is so well illuminated you can see the Jockey, its cannon thing and the floor around it perfectly. In all close shots, it's suddenly pitch black and all we can see is the small areas lit by the crew's helmet lamps.
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. (01:21:35)
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)
Continuity mistake: When Dallas, Kane and Lambert are exploring the alien spacecraft, you can see that there are wipe marks inside of their helmets that change between shots, most notably on Kane. This is because the helmets were built with out sufficient exhaust systems for the actors. Of course, the characters wouldn't be able to wipe the inside of their helmets with them on.
Continuity mistake: After the alien leaves Kane's face and the rest of the crew are looking for it in the infirmary, there is one shot that bears re-watching. When Ripley is looking upwards over the prone Kane, you begin to see the dangling tentacles of the alien in the background. At the same time, the collar on her outfit begins to pull downward, un-naturally, until the alien drops onto her shoulder. I believe there was some sort of string or rope fed from below, through her clothing, and was attached to the alien and was pulled to have the creature drop onto her. (00:48:33)
Continuity mistake: Before Lambert is killed, the alien twists its tendrils around her leg, and we see that she has sneakers on. However, when Ripley notices Lambert's dead body (hanging?) she is barefoot. [The rest of the scene was cut. According to the novelization, Lambert was actually intended to be shown completely naked and sexually ravaged. Director Ridley Scott had toyed with the idea of creating the illusion of the Alien having raped her before her death. He thought better of it and cut the scene. Still a mistake, but there's why.] (01:33:40 - 01:34:25)
Continuity mistake: When Ash calls Dallas to the infirmary, Dallas appears in a white shirt that has a blue patch or tag above his left/front pocket. Then he and Ripley leave the infirmary and have an argument in a corridor. Suddenly, Dallas' shirt has a gold patch where the blue one was moments earlier.