Plot hole: The Doctor says he used the fast return switch to take them back to 1963; however, the last place the TARDIS had been before landing on Skaro was 100,000 BC.
Plot hole: Yartek tried to disguise himself as Arbitan by wearing Arbitan's robes and pulling the hood over his giant rubber head. Strangely enough, no-one seems to notice that "Arbitan" is now suddenly speaking with a completely different voice, and now has a two-foot-tall-head.
Plot hole: In episode 4, we're informed that Susan and Sabetha traded their travel dials for firewood, and Ian trades his for furs. They do not take them with them into the caves later on. This only appears to make sense from an out-of-universe perspective: Terry Nation needed the characters to part with their travel dials, so they couldn't have just escaped after collecting the key.
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 ★