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.
Character mistake: When Ripley interfaces with Mother for the first time and sees the special order, an instruction reads as "Insure return of organism" rather than "Ensure return."
Other mistake: When Ripley is trying to deactivate the self-destruct mode, the instructions she follows on the container are actually just the French interpretation of the instructions she read to activate self-destruct before.
Continuity mistake: When Dallas uses the pen to catch the acid, it melts the back of the pen to the point that it's deformed and smoking. When he hands the pen back to Brett, the back of the pen is no longer deformed at all but it's still smoking.
Factual error: When the crew shoots Kane's body out into space, the door opens up and "explosive decompression" causes Kane's body to fly out into space. At the beginning, the body slowly rotates. Then as it moves further away, the body begins flipping much faster. The reason something would increase speed in rotation like that is due to aerodynamics. An object traveling through space would simply keep the same rotational velocity it begins with since there is no air or other influences (gravity, etc.). The explosive decompression may cause it to increase rotation speed, but by the time it begins to flip, any air would have dissipated into space and not work as a column of air/wind to force the body into a flip.
Revealing mistake: Mirrors were used to make the corridors appear longer, early in the film when Brett is complaining to Parker about the way they are treated by the company you can see their reflections in the mirror behind them as they walk down the corridor. It's only for a second as they are moving off camera but you can see them in their white overalls.
Deliberate mistake: After Ash's body is incinerated, the interior walls of the Nostromo appear more metallic and grey than they were before. According to Ridley Scott, this was done deliberately to make the alien's presence appear more menacing.
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 the dead facehugger falls onto Ripley in the medical room, it lands on the floor with its legs up. The distant shot shows its tail has looped under its body, but the close-up shows the tail entirely straight.
Continuity mistake: When Ripley backs into the shuttle closet you can see three axes on the wall next to her, when she starts to get into the space suit there are only two, then when she puts the helmet on there is only one.
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.
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: In the air duct when Dallas touches the slime, the amount of slime on his hand changes between shots.
Audio problem: When Tom Skerritt first "interfaces" with Mother after being awoken, he says, "Good morning, Mother" - it is not even close to being Tom Skerritt's voice. According to the book 'The Making of Alien' this line was dubbed in by Ridley Scott as Tom Skerritt wasn't available at the time.
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.
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).
Suggested correction: As was standard, the Narcissus (which was the name of the shuttle) was designed to carry a crew of three, although the interior could be easily modified to seat more crew members if necessary. For long-duration travel, the shuttle contained two stasis capsules, although long-range interstellar transit was not the vessel's primary purpose. So in a life-or-death situation, four people intending to use it to get off the Nostromo isn't a plot hole.
I'm not sure I understand the correction. The reason Ripley rules out escaping on the shuttle at first is because it does not accommodate four crew members. When she later changes her mind after they've destroyed Ash, the natural assumption is that the shuttle has become a viable option now that they're down to three, but we later see that wasn't actually the case, because it only has two cryotubes. A better argument, I think, is that at that point they simply no longer cared.
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.
Revealing mistake: At the start of the film where we see the cockpit for the first time, you can see the camera shake as it bumps into something whilst it pans towards the seats. The sound of the bump can be heard as well.
Audio problem: When the crew are dining together just before Kane meets his grisly end, the scene cuts from a long shot, where Parker is saying something, to a closer shot, with the conversation continuing as before. The problem is that Parker's voice can still be heard, but his lips aren't moving.
