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?
Factual error: Servalan's space station is shown rotating at a fairly fast clip. But the stars in both her office window and in the courtroom window are stationary. Because the station is spinning much faster than a planet's normal rotation, the stars should be visibly moving.
00:00:35 - 00:03:10Jean G
Factual error: Avon and Vila watch the rocket launch from the surface of the planet. The rest of Liberator's crew also watch it from the flight deck, and somehow their view from orbit is at exactly the same angle from which Avon and Vila are seeing it: a ground-to-air shot.
Plot hole: Avon drills the last hole through the bomb's tubing and then, with the drill still in place, has to hunt down the dropped rod needed to block the plunger. Tense drama ensues while it's found and inserted, though simply leaving the drill bit in there would have worked just as well.
Deliberate mistake: In the escape scene near the end, an explosive charge that went off too soon knocked Paul Darrow over - and briefly out of the shot. Because he was able to get back up and keep running, the accident was left in, though he's said it was fortunate there was no microphone on him at the time, as he uttered a few words that were "definitely not rated PG."
Revealing mistake: When he sits on the floor in front of Servalan, Jarrier's earring falls off. He fumbles at it briefly, and then the actor breaks character for just a moment, glancing nervously at the camera. When it's apparent there won't be a retake, he goes on with his lines.
Continuity mistake: Provine shoots the rebel guarding the rocket in the chest. But later, when his body is found, the man is bleeding from the mouth instead, and the blood pooled on the floor beside him changes from beside his head to above his head between shots.
00:21:10 - 00:42:00Jean G
Revealing mistake: In the control complex, Avon tosses two coin-like objects onto the electrified floor to test the grid. But the "coin" is already on the floor before the sound effect of it landing can be heard, and the mini explosions the coins set off is the same footage both times.
Revealing mistake: Blake hands Cally a photo of Docholli, supposedly obtained from Zen. It's a publicity still of the actor that's not only in black & white (how low tech), but Cally has to hold her thumb rather conspicuously over the very 20th Century necktie he's wearing in the photo. You can see a bit of it anyway.
Plot hole: The IMIPAK weapon marks its victims and then kills them with a secondary device. But it's inconsistently selective. When Servalan kills the guard with it, Blake and co., marked and standing nearby, are unharmed. But Rashel later warns Travis not to push the button because he and Servalan are marked and would die too. (That the weapon's range is "adjustable" is nowhere mentioned or implied. Servalan doesn't change a thing before she fires it).
00:43:55 - 00:46:30Jean G
Continuity mistake: When the crew teleports up at the end, the shirtless Vila arrives in a completely different position relative to the others. On the surface, he's standing in a ring with the rest of them. When they materialize, he's hunched over and is now in the middle of their circle with the others around him.