@NovaStar finally comes through with the win! You're up, now.
(good try
@Jim Of Seattle)
Explanation of Clues:
Patterns of Force (or Nazis in Space!)
-Hint: There's a level of sarcasm in each clue.
1st Clue: How do you hide the Enterprise? Huh? That actually works?
SPOCK: Passing outer planet, Zeon.
KIRK: We want the inner one, Ekos. Plot a standard orbit, Mister Chekov, and take us in.
CHEKOV: Aye, sir.
KIRK: Lieutenant Uhura, raise John Gill on Starfleet communications.
UHURA: Captain, no response on any Starfleet channel.
CHEKOV: Spacecraft approaching from inner planet.
KIRK: From Ekos?
SPOCK: Yes, but it must be a Zeon ship. Zeons do have a crude interplanetary capability. Reaction powered. A small rocket. It is on an intercept course. That would mean it has sophisticated detection devices which neither Zeon nor Ekos should have.
KIRK: Range, Mister Chekov?
CHEKOV: Two thousand kilometres, closing fast.
KIRK: Fire.
SPOCK: Fascinating. A thermonuclear warhead.
MCCOY: That's generations ahead of where these people should be technically. How'd they manage that?
KIRK: Maybe they had help. Maximum orbit. Take us out of range of their detection range.
SPOCK: Most interesting. We were attacked by a thermonuclear missile from a planet which should have no such weapon.
CHEKOV: Orbit computed and locked in, sir.
KIRK: Execute.
The Enterprise is detected and attacked in standard orbit. To avoid future detection, Kirk orders maximum orbit to get beyond detection range. Orbit around what? The sun? Also, in Tomorrow is Yesterday, the ship's deflector shields were used to avoid detection (by radar), but no mention of the shields. It is not explained how simple "maximum orbit" avoids "sophisticated detection devices".
2nd Clue: We see proper research.
John Gill does solo Federation research on the planet, then violates the prime directive. The Nazi movement he puts in place started about three years ago, and the Federation lost contact with him about 6 months ago, so, he was submitting false reports to Starfleet for 2.5 years. Not proper research.
3rd Clue: I have a good idea. What could go wrong?
John Gill selects brutal Nazism to save a warlike race. Melakon takes over and a campaign of terror is started against the Zeons. SPOCK: Captain, I never will understand humans. How could a man as brilliant, a mind as logical as John Gill's, have made such a fatal error?
-sub-clue: except the daggers shooting out their eyes
A take on Hate stabbing out of the Zeon eyes at the Nazi. (eh, it was only a sub-clue)
4th Clue: That's a neat device, how come we never used it before or since?
The transponders.
-sub-clue: except maybe a 40 watt bulb
The rubindium crystals in the transponders are used to create a laser beam using the light of a bare light bulb.
5th Clue: After all we've done, you're refusing our help?
ENEG (to Kirk): Thank you, but go now. We must do the rest.
6th Clue: Yes, it hides your sins.
The German-style helmet hides Spock's ears.
7th Clue: The notable woman sets the standard; let's reward her.
Daras is the woman. Spock: This young lady is a Nazi, a hero of the Fatherland. We saw her being decorated.
-sub-clue: No little girls, but there was one notable girl.
ditto.
8th Clue: Exposed and Deposed. I doubt the job will be refilled.
Both Fuhrer John Gill and Deputy Fuhrer Melakon were exposed, then both got killed. The sense at the end of the episode is that Nazism is gone and there will be no new Fuhrer.
9th Clue: Doctor McCoy, you disgraceful drunk! Straighten that uniform.
UHURA: Doctor McCoy is having difficulty with that uniform, sir.
KIRK: Send him down naked if you have to. Kirk out.
(McCoy is beamed down still trying to put a boot on.)
MCCOY: Stupid computer made a mistake in the measurements. The right boot's too tight.
(guards walk in)
KIRK: The Colonel is drunk. He's had a little too much to drink.
ENEG: I see.
KIRK: Yes, he thought he would embarrass the Fuhrer.
SPOCK: Yes. A doctor should have more pride.