The Daleks - S1-E2
Visible crew/equipment: About 90 seconds into Episode Two, the shadow of the boom mic crosses Ian's face. (00:01:29)
Visible crew/equipment: (Ep. 2) When The Doctor, Jo, and Dr. Tyler are taken into Omega's palace, in the first shot of the multiple passageways (right before Jo says that it looks like Aladdin's cave) the curved chalk actor's mark is visible on the floor, then we see it again in three following shots. Note that when they're all escorted further inside, just as Dr. Tyler comments about the matter/anti-matter not making sense, Jon Pertwee looks down, presumably to make sure he hits his mark.
The Daleks - S1-E2
Visible crew/equipment: The boom mic shadow makes an apperance in Episode Two, moving across the console as the Doctor suggests abandoning Barbara.
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.
100,000 BC - S1-E1
Visible crew/equipment: The boom mic makes an quick appearance about 18 minutes into episode one. It is in the upper left corner when the camera switches from a close up of the Doctor and Susan to a medium shot of all four characters.
Visible crew/equipment: In episode one, when the Doctor is near the pyramid, someone's leg can be seen just before the shot ends.
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.
Earthshock - S19-E6
Visible crew/equipment: As Lieutenant Scott is moving up the scaffold staircase, you can see someone at the top of the screen reading a script. (01:04:20)
Visible crew/equipment: When the Ogri does attack the Doctor and Rumford in the cellar, the person pushing it is quite visible as is another crew member standing to one side.
The Daleks - S1-E2
Visible crew/equipment: Toward the end of episode one, when Ian is wondering where Barbara is, the shadow of a boom mic moves over the door behind him.
Visible crew/equipment: When Romana brings the Tracer near the jewel cabinet in episode one, the wire powering the prop can be seen at the bottom of her hand.
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 2, as K-9 seals the wall panel, watch out for the hand which emerges to hold it in place.
Visible crew/equipment: In episode two, the shadow of the boom mic crosses Jon Pertwee's head as he's giving the "epsilon coordinates" to Liz.
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 episode four, the Dalek chasing the heroes up the ventilator shaft is supported by strings.
Visible crew/equipment: In episode one, when Ian is first seen inside the pyramid, someone stumbles through the background. Some have claimed this is Barbara, but it happens too fast to tell.
The Dalek Invasion of Earth - S2-E2
Visible crew/equipment: When the rebels attack the Dalek saucer, a Dalek asks what sector the prisoners were taken from, and in the bottom left hand corner a giant boom mike comes into view.
Revelation of the Daleks - S22-E6
Visible crew/equipment: In the first scene of episode 2 you can see a member of the crew casually walking in the background.
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 ★