This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Brows Held High
His review of Angels in America, especially his ending words for the review (in which Oancitizen appears to be tearing up himself):
"For World's AIDS Day, we have to remember those who have fallen. The world only spins forward, and they will be citizens. The time has come. Bye, now. You are fabulous each and every one of you and I bless you. More life. The great work begins."
The part near the end where Kyle leaves his apartment to go for a walk.
Plus: Linkara shows up after he leaves for a cameo... and is confused about where he went...
"It's only a movie. I mean, Jesus, if I did anything good on this planet at least let me know that I got somebody to watch a fucking movie. It's— it's such a tiny thing. Such a tiny thing. It's too big for me."
Well, he fixed the reverb! ... by holding the review in a closet.
Film Brain's cameo started off berating Kyle for neglecting to expand on the film as a metaphor but veers into Film Brain's increasingly genuinely concern over Kyle's personal well-being. If you've seen To Boldly Flee, it expands on the aspect that Film Brain cares for his fellow reviewers, and it's heart-wrenching to see Kyle shut him out (off).
Film Brain: Are you okay?
Oancitizen:Yes, I understand the movie.
Film Brain: Please, Kyle, we can tal—(gets turned off)
Pretty much all the cameos are depressing. JesuOtaku shows up and suggest that they do another crossover anime review after seeing what he is reviewing (his suggested anime, The End of Evangelion, having similarities to Melancholy). He replies "Joy." but he was Sarcasm-Blind and squees over it.
When JesuOtaku corrects him that it is "anime" not "cartoon", he proceeded to blow up and angrily lashes out at him. Instead of yelling back, he quietly calls him out and says he'll leave until whatever he is going through is over.
JesuOtaku: I'm feeling so insulted right now, and this isn't you.
A subtle one, but listening to Kyle's commentary on Mister Lonely, one can't help but feel even just a little bit sorry for Harmony Korine:
Kyle: Harmony Korine is working with the upper echelons of the cinematic medium; the best directors whose work is seen by no-one. And here, he's made a story about people acting like the Greats, aiming to please an audience that may not exist. [...] Here we might see how Harmony Korine views his art; he is trying to be greater than himself, and finds solace in his friends with the same mad ambitions. [...] And so, I cannot hate this film. Yes, I mock Harmony Korine, but I'm doing so drunk on the courage of his liqour, because... I share his insecurities... and I share his ambitions.
The full episode name for Merry Christmas, Mr. Lawrence is titled "Merry Christmas Mr Lawrence: A Miserable Holiday Movie for a Miserable Year," and the intro before the title card is Kyle simply reading Time: The Year in Review, then angrily ripping it apart without saying a single word. After the title card (which plays for only a second), he quickly tries to just get 2016 over with by watching something festive... and the only Criterion film he could find of Christmas happens to beMerry Christmas, Mr. Lawrence. 2016 has clearly been rough for him.