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.
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: After Ash is decapitated, Ripley says they are going to blow up the ship. In the shot where Parker looks back, Ash's head is slanted to the side. The shot cuts back to Parker where he turns on the flamethrower and incinerates Ash, whose head is suddenly flat on the table. (01:25:40)
Continuity mistake: When Ripley is trying to re-activate Ash, Ripley flattens his head onto the ground. Her left hand is placed on Ash's head and her right hand is placed on the skin below Ash's neck. As soon as Ripley gets the head fixed on the ground, she begins to remove her right hand from the skin below Ash's neck. In the instant shot following, her hand is suddenly back on the skin below Ash's neck. (01:23:05)
Continuity mistake: After the Alien bursts out of Kane's chest, Parker grabs a knife and goes to stab it, and Ash raises his arm at him, telling him not to. The alien then runs off and visible in the back of shot is Ash still pointing at Parker with his arm raised. Then in a sudden close-up of Ash, his arm is now lowered. Although, his entire arm isn't visible, just under his shoulder, the top of his arm is still visible, so his arm is definitely not in the same position as it was in the previous shot. (00:57:30)
Continuity mistake: Near the start, when Dallas is at the entrance to Mother, one of the lights to his left, the fifth one down from the ceiling, is not lit. The next shot from inside Mother looking out shows that light is now lit. This exact same thing happens a second time when Ripley is entering mother later in the movie. These two scenes must have been shot at the same time. (00:08:20 - 01:18:35)
Continuity mistake: When Dallas is in the air vent trying to flush the Alien out of the ship he is carring a flamethrower. Right before his demise, he is told by Lambert to "Get out of there" or something to that effect. In the next shot you see him descending a ladder clearly WITHOUT the flamethrower. However, in the shot after that (when he is lowering himself to the bottom of the ladder, right before the alien gets him) he somehow has the flamethrower again (it even got reslung around his shoulder). (01:15:25)
Continuity mistake: When Ripley runs back into the control room to abort the self-destruct, one shot shows the timer reading 5 minutes. The shot then cuts to Ripley pulling a lever back to where it originally was and yells out "Mother, I've turned the cooling unit back on! Mother!" The shot then cuts back to the timer where it can be seen it has only gone down by 2-3 seconds, but all of what just happened took longer than that. (01:38:40)
Continuity mistake: Near the beginning when the Nostromo crew are debating over landing on the planet and Parker is arguing against it. Ash addresses him by revealing the company clause that states any potential alien intelligence must be investigated. He even mouths to Parker "no money." In the best shot Ash is directly behind Parker and not in a position where he could have been directly addressing Parker as the previous editing suggested. (00:12:35)