Continuity mistake: When Inga, Frederick, and Igor reach the secret library, Frederick reaches for the door knob to grasp it with his right hand, but the view from inside the room showing them entering has Frederick's right hand opening the door without using the knob.
Factual error: In the scene right after pinback shoots the beach-ball alien, we see the Dark Star space craft cruising past a planet with a sun in the background. You can see a reflection on the planet which is coming from the space craft. I'm sorry, but usually ships in space are not large enough to reflect off a planet, especially to the degree this one does. (00:48:20)
Visible crew/equipment: In the scene in which Zed & his fellow exterminators chase down several brutals on the beach, tire tracks from the camera vehicle can be seen briefly imprinted in the wet sand.
Other mistake: The Amazon's queen says she pierced Dharma's chest with her spear/lance but he's shown dying from a side wound.