Revealing mistake: The Filer vs. Filer fight in the lab is very amusing, not only because of the several glimpses of the stuntman doubling for Filer, but also because of the way the "metal" railings around the set wobble as they slam into them.
Character mistake: The Doctor gets Jo to do some mathematics to distract her. At one point she says "49 x 2=88", when it actually equals 98, then she says that "adding 10 equals 108". (In other words, Jo (Katy Manning) fluffed her line, got one figure wrong, then went back to script...).
Revealing mistake: In the UNIT tracking room, there is a flimsy railing behind the radar operators that Chinn knocks as Yates leads him off to the "direct" phone line, causing it to wobble badly. The Doctor then deals the railing another blow as he comes up to look at the console.
Audio problem: When Chinn tells the Brigadier of his agreement with the Axons, the movement of the actors around the set causes various loud wooden clumping sounds that are rather inappropriate for the organic interior of Axos.
Continuity mistake: As the Master escapes from Axos, he kills the UNIT soldier standing guard outside, whose beret falls off as he slumps to the ground. Cut to the Master standing over the corpse, and the missing beret instantly replaces itself on the head of the corpse.
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 ★