Plot hole: After Romana and the Doctor hide in the relic room, the Captain enters, then bends down to inspect the door that conceals the Shrivenzale. Unfortunately, the actor turns to his right when he does so, which make it rather odd that he doesn't see the white-clad Time Lady standing right in front of him.
Plot hole: Mr. Fibuli reports that the aircar the Doctor tried to steal is immobilized. Yet somehow, K-9 is able to activate it.
The Armageddon Factor - S16-E6
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.
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★