The Talons of Weng-Chiang - S14-E6
Continuity mistake: In episode 1, when the Doctor and Leela leave the TARDIS, the door is open and is not moving. They then walk away from the TARDIS for a few seconds. When they hear the attack on Bullard (the Cab Driver) and run past the TARDIS again, the door is magically closed.
Genesis of the Daleks - S12-E4
Revealing mistake: Whenever there's a close-up of Davros, it's very easy to see that there's a gap around his mouth where the mask should blend in with the actor's face, but doesn't. This mistake was rectified, incidentally, in Davros' next appearance in "Destiny of the Daleks."
Continuity mistake: After the Raston Warrior Robot has killed all the Cybermen, watch the dead Cyberman in the back right of the picture. His arm position changes as the robot teleports away.
Factual error: The nuclear physics in the reactor scenes is laughably incorrect.
The Dalek Invasion of Earth - S2-E2
Revealing mistake: When a rebel throws a bomb from the second floor of the Dalek saucer, notice it explodes too early and in the wrong place.
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: When the Doctor falls out of the TARDIS, near the beginning, he nearly manages to pull off the entire TARDIS door.
Revealing mistake: The explosion of Irongron's castle is obviously stock footage of a quarry explosion.
Revealing mistake: As the cast move through the transom of the space station, observe the starscape through the lower windows. At certain points you can see a thin strip of light where the black curtain used for the stellar backdrop meets the studio floor.
Visible crew/equipment: At various points in the story, the pots for the plants of the Spiridon jungle are visible. Episode two has a couple of noticeable moments, when Codal is captured and when the Doctor is led away by The Daleks.
Continuity mistake: When Wester - an invisible Spiridon - is treating Jo's arm, his shadow can be seen.
Revealing mistake: In episode one, Scaroth's 'Jagaroth skin' on his wrist flaps about. Either that's a badly fitting piece of costume...or he's suffering from severely peeling skin.
Plot hole: Peri goes to a fair bit of trouble to bolt the door on the bath house when rescuing the Doctor. When the Rani and the Master arrive, they simply open the door. Now this, in itself, isn't a mistake, as the Master has a special gadget for opening locked/bolted doors, but both the Master and the Rani seem surprised that someone is in the bath house.
Revealing mistake: At various times (especially in episodes 3 and 4) you can see actor Stephen Thorne's lips through Omega's mask (and in one profile shot you can also see his jaw), yet when his mask is removed, we find that Omega has been dissipated and has no face...
The Moonbase - S4-E6
Revealing mistake: The doors and walls wobble badly as Jamie and Ben barricade the entrance to the medical unit.
Deliberate mistake: The shot of rocks falling in episode four is used twice - once when Unstoffe is shot, once after the captain fires the cannon.
Visible crew/equipment: Near the end of episode 3 the inspector is on the plane and just before he goes to look for Captain Blade the camera zooms out and the top of the set is visible.
Other mistake: Several shots are repeated during the implosion of the priory.
Visible crew/equipment: After Rokon's message in episode four, Eldra starts ranting and raving. A BBC camera can be seen in the doorway behind the Doctor and Sarah.
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 ★