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.
Visible crew/equipment: In episode five, when Taron knocks out the Spiridon, you can see a BBC camera in the foliage behind him.
Visible crew/equipment: In episode one, when Dai Evans is on the telephone in the mine, an arm of a crew member appears to the bottom right of the screen, giving the actor his cue to speak.
Invasion of the Dinosaurs - S11-E2
Visible crew/equipment: In episode 4, when the Doctor is in the Whomobile, a dark cylindrical object passes in front of the camera in the foreground. It's not something of the Doctor's, as his hands are inside the vehicle.
The Monster of Peladon - S11-E4
Visible crew/equipment: When Azaxyr is setting his ambush for the miners in episode six, a studio light can be seen through a gap in the wall.
Genesis of the Daleks - S12-E4
Visible crew/equipment: Just after The Daleks move past the Doctor and the female Thal soldier in the corridor, a piece of lighting equipment is reflected on the wall behind her. (00:08:00)
Genesis of the Daleks - S12-E4
Visible crew/equipment: In episode 1, when General Ravon is being held at gunpoint and he says 'they won't last much longer', the shadow of the boom pole is moving on the door behind him. (00:15:15)
Revenge of the Cybermen - S12-E5
Visible crew/equipment: Quite a few times during this story arc you can see Vogans without their gold eye make-up so you can see human coloured eyelids when the rest of them is all brown.
Visible crew/equipment: In episode 4, look out for the legendary "Hand of Sutekh" - a hand (presumably that of a member of the crew) holding the cushion down in the scene where Sutekh stands up.
Visible crew/equipment: In episode four, after Marcus opens the second door in the pyramid (the one with the hidden switch), someone wearing a white shirt can be seen through the opening.
Visible crew/equipment: Episode 1: After Sarah teases the Doctor a bit when he's being somewhat moody, just as the TARDIS is suddenly thrust off its flight path (which was back to UNIT), Sarah and the Doctor are thrown about in the wonky console room (because the camera turns sideways), and the second camera becomes visible at the left side of the screen.
Visible crew/equipment: In episode one, the Doctor and Sarah crouch behind a pod to escape the android laser fire. They lie on a large brown piece of cloth conveniently placed to keep them from getting dirty.
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.
Visible crew/equipment: When Leela runs into Toos' quarters (and finds D84 leaning over Toos), we see a low-angle shot of her entering the room. Look at the brief shots of her before and after D84's line, "Please do not throw hands at me," and you'll see the front of the camera that took that low-angle shot jutting out into the doorway behind her, before it slowly retreats out of vision.
Visible crew/equipment: In episode three, when Toos talks about the disposal of robots, a crewman can be seen behind her, toward the back of the set.
Visible crew/equipment: When Leela bandages Toos' arm, a member of the crew is visible on the edge of the set.
The Talons of Weng-Chiang - S14-E6
Visible crew/equipment: The shadow of a boom mike is visible on the curtains near the stage in the final fight.
The Talons of Weng-Chiang - S14-E6
Visible crew/equipment: In episode six, when the Doctor and his friends are hiding behind the table and Mr. Sin is blasting it, look out for the pyrotechnic wire dangling from the underside of the table.
Visible crew/equipment: In episode four, when the Doctor is congratulating himself on blowing up the Swarm, the shadow of a boom mike can be seen.
Visible crew/equipment: In the first scene of episode two, as the Doctor collapses on the ground, a person can be seen moving in the back of the set.
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 ★