These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Star Trek S 2 E 1 Amok Time
Angst? What Angst?: Kirk and Spock are both awfully calm after their reunion considering that Spock almost killed Kirk.
Ear Worm: The infamous fight scene music, which became so well known that Eddie Murphy referenced it in one of his stand-up routines.
Fanfic Fuel: Fanfics have been penned on how young Spock and T'Pring felt about the Arranged Marriage and how Kirk and Spock coped with the aftermath of the kal-i-fee.
Fridge Brilliance: Kirk gets ridiculed for jumping from "biology" to "reproduction", but Spock is obviously embarrassed and what part of biology is half so embarrassing to talk about as reproduction?
Also, T'Pau says that T'Pring will become "property" of the victor. Presumably, Spock could have treated her much worse than he did and been within his rights... just like T'Pring was in pitting Spock against Kirk. She's lucky he didn't decide to go Beware the Nice Ones on her.
Fridge Horror: in Spock's final exchange with T'Pau, he responds to the traditional "Live Long and Prosper" with "I shall do neither." Did Spock mean that the civilian courts would execute him, was he contemplating suicide, or did he mean he would die of grief and guilt?
Also, T'Pring explains that she could do whatever she liked because Spock would be "gone". Did she mean "away on a mission" or "dead"?
Also, the end. Yes, Spock won't kill himself or die of grief now that he knows Kirk is alive, but he'll have the guilt of having attempted to kill his best friend for weeks, maybe the rest of his life.
Throw It In: The Vulcan salute makes its first appearance in this episode. Leonard Nimoy came up with it on set. Incidentally, Arlene Martel, the actress playing T'Pau, couldn't do the salute and had to arrange her fingers with her other hand off-screen.