Plot hole: When Ultraworld first shows up on the Liberator's screens, all scans show it isn't there. Avon explains it can't be detected because it is an artificial planet using alien technology which blocks all electromagnetic radiation from escaping. But the crew are looking at it on their screen - the ordinary visible light we use to see things is part of the electromagnetic spectrum too.
Continuity mistake: When Dayna & Tarrant are "bonding" they are not wearing their gun belts. Yet the shot of them running down a corridor immediately after escaping shows Dayna has hers on. In the next scene, it's gone again. Later Avon & Tarrant recover three gun belts from the control room.