Audio problem: When the Doctor chops a brick in half, you can tell that the brick is really made from balsa wood by listening to the sound it makes when it hits the ground.
The Talons of Weng-Chiang - S14-E6
Audio problem: In episode five, when the Doctor and Leela are in the opium den, the Doctor's lips do not match his spoken dialogue.
Earthshock - S19-E6
Audio problem: In episode two, the Cyberleader misses a button on his console, yet we still hear a beep...
Resurrection of the Daleks - S21-E4
Audio problem: Davros' lips don't move when he says, "Now for The Daleks," just before he releases the Dalek-killing virus.
Audio problem: In episode 1, the Doctor hits something on the central console (not the door control) and walks towards the door. The door doesn't open, but the sound of the door opening is still heard.
The Trial of a Time Lord 13-14 (aka The Ultimate Foe) - S23-E4
Audio problem: All of the scenes of the trial have some sort of sound problems. Among other things, sound bites from earlier on appear from seemingly nowhere, and, if you listen carefully, you can hear someone calling out the cue "Take 6", which should have been edited out quite easily, but wasn't.
Audio problem: In episode 2, the Kandyman's microphone picks up quite a bit of the Doctor's dialogue by accident.
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 ★