Revealing mistake: When the Doctor sabotages the inertia neutralizer, the wall wobbles.
Revealing mistake: The TARDIS manual Romana shows the Doctor quite obviously has a couple of hand-written pages jammed in so that they can be easily ripped out.
Revealing mistake: There are times in this episode where the strings holding up the Captain's trophies are visible. Additionally, the "billions of tons" of planet sways back and forth slightly.
Factual error: While gravitational forces can be "balanced" between planets at very specific points, the notion of balancing them completely to cancel each other out everywhere, as depicted in the Captain's trophy room, is nonsense.
Revealing mistake: The queen, suspended in the last few moments of life, can be seen to breathe rapidly and blink.
Plot hole: Mr. Fibuli reports that the aircar the Doctor tried to steal is immobilized. Yet somehow, K-9 is able to activate it.
Continuity mistake: K-9 looks slightly different in the scene in which he's spinning inside the TARDIS: notice the pattern on his collar.
Revealing mistake: The split screen used to make two Doctors appear simultaneously is apparent when the Captain's chair appears to blur while both are in shot.
Visible crew/equipment: When the Doctor and Kimus are breaking into Xanxia's room, an ordinary telephone is visible on the right of the screen.
Revealing mistake: When Pralix lifts the spanner in the composite shot, bits of debris lift up with the spanner.
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 ★