Continuity mistake: In the escape pod Ripley presses buttons to release gases onto the alien. Watch her helmet between the cuts. During the first two gas releases the inside of her helmet is foggy and streaked; cut to the alien reacting to the third gas and when the camera returns to Ripley the inside of her helmet is clear.
Audio problem: When they are looking at the molecular acid eating through the decks of the ship from the facehugger, Parker says the words "Take a look at this man!", but his mouth is saying something completely different and much shorter.
Visible crew/equipment: As the Alien drops down behind Brett (before it kills him), you can see wires attached to the Alien's back.
Continuity mistake: When the ship warms up before the crew is revived, a computer workplace is shown two times: in the second instance, an empty coffee mug sits before the right side of the screen that wasn't there before.
Continuity mistake: Just after Dallas is taken by the Alien in the air shaft, the crew are round a table discussing what they should do next. Ripley has a visible injury to her right cheek, a round swollen injury. In the next scene the injury has gone. It's possible that it was caused by accident filming the scene when she was attacked by Ash with the rolled up magazine, although that happened later in the film.
Continuity mistake: When Ripley sits in the escape pod, she secures her seat belts. As she flushes the alien the belts are on then off then on again.
Character mistake: When the crew come upon the space traveler in the derelict space craft one of them says he is fossilized. For fossilization to occur the tissue must be replaced by minerals from surrounding materials. That is why fossils are found in the ground. When the creature dies it must be covered with dirt or mud before it decomposes. Over time the minerals in the dirt replace the tissue. But the space traveler is sitting in the pilot chair, completely open to the environment and not covered with anything. The term they should have been looking for was 'mummification' or perhaps 'skeletonization'.
Character mistake: Ripley identifies herself as 3rd officer. She is actually a 2nd officer.
Revealing mistake: The amber warning lights on the ceiling start flashing before Ripley has activated the self-destruct system.
Continuity mistake: When the ground crew prepares to leave, the captain tells them to take weapons. All three crewman are in suits with side arms on hips. These weapons are never seen the rest of the movie.
Suggested correction: With reference to the side arms mistake the weapons are seen, when Kane goes to look inside the egg before he is attacked he is carrying his side arm and holding it ready.
Continuity mistake: As Mother counts the seconds down from 10, after Ripley safely shoots out into space at the end, suddenly the 8, 7, 6 etc. speeds up.
Revealing mistake: As Ripley, Lambert and Parker leave the room after decapitating Ash, Parker turns around and incinerates Ash's body. As soon as the shot starts, if you look carefully just before the flame actually touches Ash, you can see Ash's head (mostly the skin below his neck) has already melted before the flame, or even the heat for that matter, touches him. The flamethrower had only been set off a split second before the fire reached Ash and by that point the head has already began melting, so the heat made from the fire could not have melted his head that quickly.
Continuity mistake: Right at the beginning of the movie we see one side of a planet with a ring going around it pointing toward the bottom of the image, then the camera slowly moves to the other side where the ring is pointing towards the top of the image. This would only be possible if the ring around the planet has a figure 8 shape, however later in the film the ring is revealed as flat.
Revealing mistake: When Dallas is in the air shaft he shoots downwards with his flamethrower, you see the flames that he is shooting from the bottom of the ladder, but you can see a flamethrower shooting upwards from the side of the shaft and it also moves in an arc.