Continuity mistake: During the big fight scene, Roddy Piper smashes the back window of a car with a piece of wood. In the very next shot, Keith David rushes Piper and continues to fight with him. Right before the shot ends, you can see the same car in the background, smashed window and all, now at least two cars over from where they are fighting.
Continuity mistake: When Roddy Piper first puts on the sunglasses, he stops at a newsstand, where he sees his first alien. Watch as the alien guy pays for the magazine he's buying. The vendor gives him change twice, and even says different things to him each time he hands him the change: 1. "Here's your change sir." 2. "Here you are sir. Thank you."
Continuity mistake: After Roddy Piper's character spends the night at the homeless camp, he walks towards the church wearing a toolbelt. He stops and watches the Street Preacher recite what is airing on television. As the shot switches back from the Preacher to Piper, his tool belt has vanished.