Continuity mistake: Magnus Greel puts Leela in the distillation chamber and switches it on. Cue red lights, special effects, and Leela writhing about. Then the Doctor arrives and throws a battle-axe into the works. Sparks fly, and the machine stops, presumably broken. Later, however, when Greel is pushed into the chamber, it turns on and does its thing just as if nothing had happened to it. Oh, and the axe thrown earlier disappears too.
Revealing mistake: Watch really closely when Leela throws the knife at one of the robots. You can see the knife fall to the floor about a second after she throws it. Then, of course, the next shot shows the knife sticking out of the robot's chest. Guess Leela isn't quite as good a shot as we thought.
Visible crew/equipment: When Leela runs into Toos' quarters (and finds D84 leaning over Toos), we see a low-angle shot of her entering the room. Look at the brief shots of her before and after D84's line, "Please do not throw hands at me," and you'll see the front of the camera that took that low-angle shot jutting out into the doorway behind her, before it slowly retreats out of vision.
Factual error: Giuliano explains to Sarah that he thinks the world is round as though this were radical. But this was the common belief throughout the late Middle Ages. The argument was about how big the Earth was and the ignorance about the existence of a continent between Europe and Asia.
Revealing mistake: When Taren Capel is modifying a Voc robot, there is a shot of the robot's agitated hands as he reassures it. On the robot's silver gloves, the "Marigold" logo is visible. ('Marigold' make rubber gloves that are used when washing dishes). Perhaps that particular Voc robot had been assigned to dish-washing duty that day...
Continuity mistake: In episode 1, when the Doctor and Leela leave the TARDIS, the door is open and is not moving. They then walk away from the TARDIS for a few seconds. When they hear the attack on Bullard (the Cab Driver) and run past the TARDIS again, the door is magically closed.