Deliberate mistake: After Ash's body is incinerated, the interior walls of the Nostromo appear more metallic and grey than they were before. According to Ridley Scott, this was done deliberately to make the alien's presence appear more menacing.
Deliberate mistake: During the space battle, one of Drax's men gets his back pack blasted. (1:46:37) His entire pack explodes so that his jet pack and life support are destroyed. But as a result of that blast, all the parts from his suit FALL DOWN! Even though there's no gravity.