Continuity mistake: In episode 4, approximately 5 minutes from the end of the story, Soldeed is shot after he pulls the lever that sets the complex on overload, and then crumples to the ground dead beneath the lever. Then, after the Doctor and everyone else get out of the complex, we see a selection of shots taken inside the complex - one of which is the room with the lever that Soldeed pulled, except he's no longer there...
Continuity mistake: (End of Ep. 3 and start of Ep. 4) When the Third Doctor fights the dark side of Omega's mind, the rings that the Doctor wears on the pinky fingers of both hands switch to his ring fingers, then back again to his pinky fingers, between shots. Then as Omega chokes the Doctor, the ring on his right pinky vanishes between shots.
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Plot hole: Sarah is transmatted down to Voga after being injected with alien poison by a Cybermat. According to the Doctor, the transmat will recognise Sarah's human molecules and separate and reject the (non-human) poison molecules. As clothing fabrics tend to made of non-human molecules, how come Sarah and Harry didn't arrive on Voga stark naked?
Plot hole: In episode four, Merak expounds on how only the Doctor and Romana can get into the TARDIS, despite the fact that he shouldn't even know what the TARDIS is. His insight continues in episode six, where he talks knowledgeably of the sixth segment of the Key to Time, despite having been told nothing about it.