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)
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)
Revealing mistake: They use the same shot three times when showing the acid eating throughout the ship. After they try to cut the finger off the face sucker, acid begins to burnt through the decks. When they have gone down 1 deck and look up they see where the acid came through. They then move down 1 more deck and look up again. The acid is just beginning to burn through. Then they look up again and it is the same shot that was used before. The same hanging acid on the right with the drip on the left. After the acid has neutralized, they look up at the hole and it is the same shot again. (00:39:50)
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. (01:18:40 - 01:20:00)
Revealing mistake: When Ash attacks Ripley and Parker beats him off, the android gets up again and tackles Parker. Look closely as Parker crawls up against the wall...the body of Ash isn't a body at all...it's half a mannequin that doesn't even have a lower body connected to it, and it is visible when Parker's legs spread and you can see that there is nothing under Ash's torso except a big hole where the lower half should connect. (01:23:45)
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)
Factual error: In the opening scene we see a bobbing bird on the table. These birds require a wet beak to work thus the glass of water. We find out that the crew is half way home when they are awakened. Later we find that they are 10 months from home, so they must have been travelling for 10 months already, meaning the bird has been bobbing for all that time and the water has somehow not evaporated.
Plot hole: The shuttle "won't take four" crew members. Considering it only has two cryotubes (and hypersleep appears to be necessary for any hope of survival), it doesn't seem to accommodate three people, either. (Admittedly I would still go for it, too, if I were up against a 7-foot-tall acid-blooded alien monster with two sets of jaws, but there doesn't seem to be much difference whether there's three or four people onboard).