Visible crew/equipment: (Episode 5) After The Daleks plan to organize a full-scale search of the jungle at daybreak, when it cuts to The Doctor and Ian, the shadow of the boom mic moves around at the left side of the screen. (00:16:35)

Visible crew/equipment: Near the end of episode five as The Daleks plan their attack, a BBC camera can be seen in the background on the right. (00:21:20)
Visible crew/equipment: (Episode 6) At the very end, after Vicki and The Doctor have watched Barbara and Ian's return to 1965 on the Time-Space Visualiser, when Vicki hugs The Doctor the moving boom mic casts a shadow at the top, left of the screen. (00:24:30)
Visible crew/equipment: In episode four, when Ian and the Doctor descend the stairs into Frankenstein's lab, you can see a boom operator and mic behind Ian, at the left side of the screen.
The Daleks' Master Plan - S3-E4
Visible crew/equipment: At the beginning of episode 2 when The Daleks are talking, a stage light is reflected on one of The Daleks.
The Daleks' Master Plan - S3-E4
Visible crew/equipment: In Episode 2 when Marc Cory and the other Ambassador are talking, a figure who appears to be wearing Space Security Uniform (and this isn't Nicholas Courtney) and a stage hand walk by, and you can also see the end of the set.

Visible crew/equipment: In the fourth part, as the mortally wounded fighter is falling against the back wheel of the cart, the camera is positioned low and its shot is panned upwards, revealing the top of the cyclorama, a large concave backcloth that has been pulled around the studio walls (presumably BBC Studio 1) to give the impression of daylight in these studio-shot but supposedly external scenes.
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.
The Evil of the Daleks - S4-E9
Visible crew/equipment: When the Doctor and Jamie enter the secret room watch the top left corner. A boom mike shadow appears and then moves out of shot.

Visible crew/equipment: Episode 5, while Zoe and Jamie are at the Weather Control Station, when they hear the Ice Warrior approaching they both hide, and the actor's T-mark is visible on the floor. (00:18:00)
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)
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: When Liz and the Brigadier are arguing toward the end, a shadow moves in the background. It's in the wrong place and too soon to be the Doctor returning.

Visible crew/equipment: (Part 3) After Omega has revealed himself to The Third Doctor, Jo, and Dr. Tyler, when he begins to speak privately to The Doctor the camera casts a shadow on Omega's body. Then after Omega turns around the boom mic dips into view at the top of the screen. And when Omega starts walking forward, the shadow of equipment (presumably the boom and mic) is moving on the far wall, near the lower left of the screen. (00:03:10)

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.
Visible crew/equipment: You can see the reflections of the camera crew in the monitor used to display the First Doctor (William Hartnell). (This is especially noticeable in episodes 2 and 4).
Visible crew/equipment: When the group are thrown into a dungeon in Omega's palace, you can see tape in the corners which is holding the set together.
Visible crew/equipment: In episode four, the Dalek chasing the heroes up the ventilator shaft is supported by strings.
Visible crew/equipment: After the Doctor recovers from his coma, he gets up and stands at the console. A reflection of a crew member can be seen in the shiny part of the central column.
Visible crew/equipment: As The Daleks plan to release bacteria into the atmosphere, a crew member is reflected in the glass box containing the bacteria.
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 ★