Other mistake: The voice of Mother saying the self-destruct sequence has been activated is heard before Ripley pushes the red button of the last of the four mechanisms used for that purpose. (01:35:58)
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).
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: 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.
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: You can see the blood was initially thrown on John Hurt instead of coming from underneath his shirt. You can also see the underlying prop wrap that was used for the blood exploding out of him just before you see the alien pop out. (00:56:56)