Well done ItsGreen! Man Trap and Trouble with Tribbles it is!
Clue # 1
In which two episodes are old-fashioned pills recommended for a different one of our heroes, in both episodes?
McCoy has sleeping tablets in MT.
McCoy gives Kirk a pill for his headache in Tribbles.
Clue # 2
In both these episodes, the pills are in the hands of our resident doctor.
McCoy - administer to himself and to Kirk.
Clue # 3
In both these episodes, one of our regulars is seen to be consuming, be it food or drink.
Kirk eats on the bridge in MT and drinks at the K7 bar.
Clue # 4
Both episodes feature a character who wants other characters to leave.
Crater wants the Enterprise to leave, Baris wants the Klingons to leave.
Clue # 5
Both episodes refer to poison or poisoning.
Darnell supposedly has alkoloid poisoning, Darvin poisons the grain.
Clue # 6
Both episodes feature creatures who feed, albeit different substances in both.
The salt vampire feeds on salt, the tribbles on the grain.
Over to you ItsGreen!