Deliberate mistake: When the Alien appears behind Brett, we first see its tail lowering before the rest of its body, even though the tail is presumably how the creature was being suspended in the air. Immediately after chomping Brett's head, he and the creature are lifted upwards, again presumably by its tail, though it's not long enough to carry them the implied distance and it's unclear what it has latched onto in the first place. This scene starts a tradition of sorts, as both 'Aliens' and 'Alien 3' feature their own scenes in which an Alien grabs a victim and both are subsequently lifted upwards by a great height, presumably by the creature's tail, and the mechanics by which this is possible and even where exactly they're going off to are always obscured to the point where the creature may as well be wearing a jet pack.
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)