Continuity mistake: Just after the doctor started the post mortem on that little girl, the front of his gown is covered with blood. Yet, a few seconds later, after the two other guys appear, his gown looks better, with less blood. And during the whole post mortem scene, the blood spot actually changes its size a few times. (00:17:55 - 00:19:55)
Continuity mistake: When Ripley is looking for the Alien in a room full of pipes and chains, she spots what looks like the head of the Alien and slowly walks towards it, talking to it as she goes. When she smashes it with a metal pipe, loads of bugs fall out and it's a completely different pipe we are looking at, it's not smooth and long but a corner piece.