Visible crew/equipment: While The Doctor and Zoe are on the SIDRAT, The Doctor expresses hope to get the hang of its controls. When the SIDRAT materializes, in the shot facing the door as The Doctor pokes his head out to exit, the camera turns toward the right and there's a reflection of the moving camera and the camera operator walking behind the camera, at the right side of the screen. (00:08:25)
Plot hole: Despite being asked to memorise all the locations and war zone commanders, Zoe's photographic memory lets her down: her first words to the Mexican leader are 'Who are you?'.
Plot hole: The map of the "War Zones" where the Aliens are conducting their War Games can be seen several times in this story. The map is visibly divided into 11 zones. Yet, during this story, the "War Zones" visited or referred to total THIRTEEN.
Continuity mistake: The end of episode 7 does not match the reprise of the story at the start of episode 8. The Doctor, Security Chief and guards file into the SIDRAT in a different order.
Factual error: The Doctor meets Jamie at a time after the Battle of Culloden. But here Jamie says he met him in 1745. Culloden took place in 1746.
Revealing mistake: Episode 6, while in the barn Von Weich asks Moor (played by David Troughton, son of Patrick, who plays The Doctor) to retrieve the monocle in his pocket. Then, when Von Weich continues with his plan, in his closeups we can see a vertical piece of mesh tape over the actor's right eye. (00:13:05)
Revealing mistake: When the resistance are storming the landing bay, one of them punches at least a foot to the right of a guard's face, but he still collapses.
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.