Revealing mistake: K-9 has a bit of difficulty in the mansion in episode two. The thread pulling him is visible and Baker has to help him over a flagstone.
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.
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.
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.
Visible crew/equipment: When Liz and the Brigadier are arguing toward the end, a shadow moves in the background. It's in the wrong place and too soon to be the Doctor returning.
Other mistake: The power output in the Doctor's shed reads "Megga Volts" instead of "megavolts."
Revealing mistake: In episode 5, when the Doctor kills the Primord with the fire extinguisher, he says 'he's dead this time' but the Primord is breathing. (00:07:10)
Revealing mistake: In episode 3, when the Doctor is squaring off against the drooling madman, the madman is inside the perimeter railings. When the soldiers shoot him and he 'falls', however, he has moved outside the railings, enabling the stuntman to jump safely. (00:10:40)
The Caves of Androzani - S21-E6
Revealing mistake: When the Doctor is looking for a way to break through his manacles, he brushes against the machine with the bright light that he eventually uses to cut them. When he does, it wobbles when it obviously should remain motionless.
The Daemons - S8-E5
Continuity mistake: After completing the third summoning ritual, the Master turns towards the spot where Azal is about to appear. He has his arms lowered and Jo is stood to his left. In the next shot his arms are up, and Jo has moved to being in front of him.
Revealing mistake: When Fenric (having possessed the body of Judson) knocks over the chess pieces on the board, watch one piece (The King) in particular. You can see a 'hinge' made of white sticky tape attached to the board and the base of the chess piece, presumably there to stop the chess piece rolling away onto the floor.
The Trial of a Time Lord 9-12 (aka Terror of the Vervoids) - S23-E3
Revealing mistake: In episode 12, while the Vervoids are dying, look out for the ones wearing sneakers and tracksuit pants (complete with drawstrings)...
Revealing mistake: In episode four, the camera wobbles when the Doctor brings the gun to Stael.
Revealing mistake: When Vira emerges from the hibernation chamber, the Styrofoam that forms the pallet squeaks.
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.
Genesis of the Daleks - S12-E4
Continuity mistake: When Sarah falls from the scaffolding, a plank of wood saves her from death. Trouble is, she fell a foot from the outside of the scaffolding and most of the plank was inside the scaffolding, therefore her feet would have hit it and she could only have landed with her head pointing inwards. But when we see her, her head is pointing outwards. (00:01:25)
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 ★