Yes, finally
@Phaser Two got the right answer.
Let That Be Your Last Battlefield (all clues are in the Captain's Mess with Kirk, Spock and Bele):
1st Clue: After dinner drinks, and drinks, and drinks...
Three beverage bottles (green, yellow, and blue) are on the table in front of the men.
2nd Clue: Drinking is punishment enough for you.
Bele just highjacked the ship, and Kirk resorted to the ship's self-destruct mode to stop him. Then instead of throwing him in the brig, he invites him for drinks. WTF?
3rd Clue: Is your glass half full or half empty?
Kirk fills Bele's glass to about the halfway mark; plus this is also reference to the half and half nature of Bele's appearance.
4th Clue: Does Spock drink or not?
Even though there is a small glass with yellow beverage in it in front of Spock, we don't see him drink it, rather he sits with his arms folder at his chest.
5th Clue: While drinking, Kirk completes his mission.
Kirk is informed by Scott during drinks that the decontamination of Ariannus was completed, which was his original mission in his opening log entry.
6th Clue: Request denied.
Also during drinks, Uhura informs Kirk that Bele's urgent request to take the prisoner Lokai to Cheron was denied with great regret by Starfleet Command.
7th Clue: Kirk is not on the right side of the issue.
When Bele tells Kirk "It is obvious to the most simpleminded that Lokai is of an inferior breed." Bele explains it Kirk that it is because Bele is black on the right side and Lokai is white of the right side. Kirk says he doesn't see the difference (which implies that he is inferior as well; he is also not black on the right side).
There was three more sub-clues, but these are not from the same scene, hence only sub-clues to the episode. I hope the further information is useful:
a. Not the correct
intruder. (so, there could be an intruder on the ship.)
Bele for a moment is an intruder when he is deposited on the bridge.
b. It sounds like you are
running away from this challenge. (someone's running away)
Lokai runs away from Bele starting their famous jog around the ship.
c.
Two of the clues have
double meanings. (two/double seems to be important). Clues 3 and 7 have a play on words hidden in them.
Bele and Lokai are two of a kind, each with two halves of skin coloration.
