Visible crew/equipment: When Romana brings the Tracer near the jewel cabinet in episode one, the wire powering the prop can be seen at the bottom of her hand.
Deliberate mistake: Tom Baker has some wounds on his lip (caused by actor Paul Seed's dog) which appear in episode one and four in the TARDIS scenes and disappear for the rest of the episode.
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.
Deliberate mistake: The shot of rocks falling in episode four is used twice - once when Unstoffe is shot, once after the captain fires the cannon.
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 ★