Here's my answers to the last round:
Clue # 1 I think this is the only time the Enterprise follows such a route.
This is, I believe, the only time we start an episode at a planet, not actually visiting it/beaming down, and then LATER reversing course and then visiting it.
Clue # 2 Unlike the back and forward in 'Amok Time' and 'Let That Be Your Last Battlefield', this course change moves the story along.
The course change moves the story along because by doing so, we visit the planet, and the source of the episode's problem.
Clue # 3 The course change is due to a mystery of sorts
Van Gelder's behaviour, unable to speak, and his position as colleague to Dr Adams, not an inmate, all prompt concerns from McCoy. The mystery man is to be returned to the colony, thus a course change is required.
Clue # 4 A similar route is taken in one or two episodes, but that is to pick up landing party personnel. This is a direct course change, which wouldn't/shouldn't have happened, if it weren't for a strange occurrence
In episodes such as That Which Survives, Friday's Child, The Paradise Syndrome and probably others, we return to the planet we orbited at the beginning of the episode, to pick up our heroes. In Dagger of the Mind, we would be none the wiser of Adams' experiments, if Van Gelder had not escaped.
Clue # 5 This is one of only two occurences, which feature this particular landing party 'grouping'.
I forgot about Shore Leave. But to be specific, this and What Are Little Girls Made Of? are the only two episodes in which Kirk beams down with a female crewman alone, as a pair, AND whilst other landing parties beam down later, they are the first to beam down and investigate.
Clue # 6 The grouping isn't character specific so much as gender specific
Indeed, as above.
Clue # 7 This episode also features the only time such a story-telling device is used in TOS
Kirk's Christmas flashback, which isn't really a flashback.
Clue # 8 One out, one in.
Noel leaves the security area just as Spock beams down to it.
Clue # 9 A 'romantic' interlude is cut short
Spock's amusing interruption.
Clue # 10 But then again, appearances aren't everything.
Kirk isn't really in love with Noel. Adams created this.
Clue # 11 No redshirts die on this occasion
Indeed.
Clue # 12 But a guest star does
Adams, of course.
I like your clues for 7 and 8 though
