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Other mistake: The Cyber Leader is supposed to follow the Master's footsteps exactly in order to get across the chessboard. He doesn't. This cannot be classed as a character mistake because the Cyber Leader knew what was involved. I believe this mistake was caused by the actor not being able to see the chessboard through his helmet.
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 ★