Continuity mistake: When Vargas beams up to the Liberator just ahead of Blake, Gan & Vila, he challenges them when they arrive from the other side of the room - by stepping out of the teleport bay. But they're standing in the teleport bay, and Liberator has only one. So exactly where is Vargas standing?
Plot hole: Travis, dressed up as the supposedly disabled dissident Shivan, fools Blake and the rebellion leaders far too easily. His head bandages completely cover his mouth (how did he eat?) and his glued-on glass eye is so obviously fake it's laughable. If we noticed, why didn't they?
Continuity mistake: Just before Scorpio crashes, Avon grabs Orac and teleports to safety. When they're still aboard the ship, Orac has several wires hanging loose from underneath. When they materialize on the planet, however, all the loose wires are magically repaired and no longer hanging.
Plot hole: When the Liberator returns to the planet, Travis remarks that their orbit is too far away to use their matter transmitter. Since Travis had only found out that they even HAD a matter transmitter (which the Federation hasn't managed to develop yet) when he spoke to a technician just before that, how would he know what the range was?
Visible crew/equipment: That main console! The uppermost of the flight consoles of Liberator isn't fixed down in this episode, and wobbles almost every time it is touched, and not just small wobbles. Watch for the 10 seconds or so after Jenna says "Eventually I might just be able to get her to start and stop", and you'll wonder how she didn't knock the entire prop off whatever it's sitting on and onto the floor.
Continuity mistake: During the firefight in the detention corridors, the blaster holes in the metal wall Jenna's firing toward keep changing, sometimes disappearing altogether. One of them is created twice, appearing as the troopers duck out of sight, vanishing and then reappearing in the same spot when Jenna fires again.
Plot hole: Avon delivers his summation of the crimes and the murderer's identity to the Ortega's crew - with his back turned to the guilty party the entire time. This gives the killer ample time to pull a gun on them. But it's also egregiously out of character for Avon, whose suspicious nature bordered on paranoia and would never have allowed him to be so careless.
Revealing mistake: Stock footage of the London's launch from Earth is run in reverse when it lands, supposedly 8 months later, on Cygnus Alpha. What are the odds that a remote penal planet will have a launching pad with configurations, lights, buildings and background terrain all completely identical to the launch stage on Earth?
Factual error: Tarrant fails Astronomy 101 here, just as Travis did in the first season. He tells the clerk, "I'm surprised you've heard of it (the FSA), if you're from another galaxy." The Tharn and his minions were not extragalactic; they were from other planets in our galaxy.
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.