
Genesis of the Daleks - S12-E4
Continuity mistake: The Doctor's big brown overcoat was taken by the regular Kaled army in episode one and disappeared. In episode six, the Doctor goes into the incubator room and comes out with his brown overcoat magically restored.

Genesis of the Daleks - S12-E4
Deliberate mistake: Chief of Security Nyder wears an iron cross on his uniform which mysteriously disappears in episode 3 - apparently the producers felt it was too close a reference to Nazism so it was removed from the show. (Source: DVD commentary).

The Sontaran Experiment - S12-E3
Continuity mistake: In Episode 2, when the Doctor calls Harry from the Control Room and Harry enters the room next to the Cryogenic Chamber, there is an oblong yellow panel next to the door. It extends from about Harry's waist line to about 200mm below the top of the door. But in Episode 3, when Noah calls Vira from the control room part way into his transformation, and everyone runs into the adjacent room, the panel is mounted differently. It now extends from about Harry's mid-torso, to the top of the door frame. (00:03:35 - 00:09:32)
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 ★