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Narm / Valvrave the Liberator
For some, Haruto revealing his transformation into a vampire by biting L-elf in the neck during the The Stinger was this.
Occasionally, the blood won't appear scarlet red, but as if it's been diluted with water.
The anime-girl who appears next to the question about resigning as a human was rather funny to some people. This was in the middle of an otherwise dramatic and suspenseful scene. Then again, it seems purposeful going by her openly flippant behavior in later episodes. During the last part of the ED sequence she can be seen again above the seemingly disassembled Valvrave robots.
A-Drei's constant screaming of L-Elf's name in rage. At one point, the sound he makes as he does so can be closely approximated as "ERRRERUFUUAAAAGHHHH~!!"
L-Elf killing a room full of armed soldiers. He then proceeds to run around the whole place like Solid Snake, pulling off explosives and smoke bombs seemingly out of nowhere. It's as improbable as it is hilarious.
Pretty much everything that happens in the second part of Episode 4. Between Shouko trying to prove her word by stripping, Senator Figaro instantly turning into a Large Ham moustache-twirling villain, and the students declaring independence with their school becoming a new nation (which promptly gets physically cut off from the Dyson Sphere by Valvrave), this show is turning into something where logic has no place. But it's ridiculously amusing.
Senator Figaro has one Crazy Awesome line that really summarizes the show: "Call me Moses. I'm gonna split this sea of students before your eyes."
The uniform of the Dorssians, which looks almost exactly like those worn by the ineffectual antagonists in Ixion Saga DT. Can't unsee!
A-Drei's line from the end of Episode 6: "L-Elf... for the sake of our friendship, die!"
Haruto's angsting about being a "monster" and "no longer human" is getting kinda funny. He gets to protect his friends, drive a kickass Humongous Mecha, have a nifty Healing Factor, jack other people's bodies and be a Chick Magnet. There has yet to be any real downside to being a Valrave pilot shown. The fact that this gets pointed out by Saki (who revels in it instead) and Aina (who gets killed for being the voice of reason) doesn't help. Hopefully Aina's death will motivate him to get over it. Actually, it's not even clear why the robots ask like that (or at all, really), rather than "we just need to inject you with some nanobots that let you drive this thing. And they will heal you if you get hurt. That ok with you? Yes/no"
It's worth pointing out that Haruto has lost control of himself twice, once nearly hurting his close friends. Of course, even if he does snap and bite someone... he just swaps bodies and he always seems calm afterward, so he could just bite his body again if he wanted to. Seems embarrassing at worst.
After a third unprovoked "episode" it is revealed that Haruto's Valvrave is hungry for something.
Episode 10 makes Haruto's curse accidentally hilarious. He was afraid of hurting his friends as his Berserker Mode aimed to bite other. In the episode's second half the curse activates but this time berserker Haruto rapes Saki. That escalated quickly... This scene is responsible for several jokes such as "Valvrape."
Kyuma's screaming in anger in episode 8 wasn't originally narmy, but one group's subtitles of that scene—translating "chickishou" as "fuck"—and also having the font gradually increase in size as he screamed made it into this.
Also in episode 8 we learn the supposedly pacifistic JIOR stocked their modules indoor sea with battleships. It's not surprising the students didn't know about them....as it's hard to imagine what the point would be. The defensive utility of warships in that scenario is almost zero.
That is, unless you remember that Sakimori is most-likely a facility meant to find potential Valvrave pilots under the guise of a high school. So some otherwise rather odd defense protocol would in that case make sense. Also, if an enemy who's main weapon are armed flying mecha manage to break into your module, then the large and very destructive mounted guns you'd usually find on warships suddenly become very useful.
Ep. 8 also has a scene where Haruto gives a lecture on the power of hope to L-Elf... by referring to L-Elf as 'bitter coffee' that is balanced by 'sugar'. Cheesy, but more appropriate than not given L-Elf's occasionally random food talk.
Episode 9 has Kyuma seeing Aina's ghost while piloting his Valvrave unit for the first time. It's a scene straight out of Mobile Suit Gundam.
In episode 12, Dorssia's brilliant strategy for defeating the Valvraves is to basically hump them with heated coils attached to the Waffe units' shields. Or as Saki herself puts it when they attack Raizo: "They're ironing him!" (Wouldn't that make them Waffe Irons?)
Saki doesn't care about being raped by cursed Haruto. Instead in season 2's beginning she suggests Haruto doing it again if he needs it. This is more awkward in the manga when there is a 1 page angst and then we go to a happy montage. When Haruto tells Saki he wants to remove his curse so that he will never hurt her again, Saki instead becomes sad because the curse was their "bond."
L-Elf shooting Marie in episode 15 just because she knew the secret of the immortality (even though Cain already knew about it) seemed as random as Sōsuke Sagara from Full Metal Panic! shooting for trivial reasons. Except not even Sosuke used real bullets!
Episode 17 has the appearance of Haruto's dad as a one-dimensional crazy scientist who experimented on the children of his co-workers and created the Valvrave robots. During their meeting, the scientist father generally acts quite goofy towards his son and his creepy concern for Haruto is played up almost as Black Comedy, with him having a portrait of Haruto's DNA instead of a photo and making exaggerated gestures or strange proclamations about evolution, including casually dismissing the gene-splicing of children because he had permission. The fact that he does all this while having the mustache of a 70's porn star and with a jovial grin on his face makes him especially hilarious to many fans, though that's probably part of the intended effect.
L-Elf's depression in episodes 19 and 20 might be understandable but it doesn't stop from being hilarious. In one scene he has written dozens of plans involving how he could have saved Lieselotte covering the walls from a room with a single marker. In episode 21 what was supposed to be a Tear Jerker was ruined by him floating around without caring about whatever was going to happen.
What makes it even more hilarious is that he somehow wrote on the ceiling even though the gravity is clearly turned on.
In Episode 22, when while they are stuck in a crater on the Moon, L-Elf and Haruto have a fight due to their angst, repeated traumas and frustration at not just each other, but the world. What makes it impossible to take serious is that they are both dressed in extremely bulky space suits the entire time, which makes them look extremely overweight.
Not to mention the CG animation. The CG in Valvrave has actually been highly praised so far, but what works for giant robots doesn't work for bright orange marshmallow suits with human faces in them. That is to say, faces, as they didn't bother animating their necks, so the two boys kind of look like squishy robots with holographic human heads.
Episode 23 has Amadeus making a face very similar to the YARANAIKA? face after his throat is slit.
Not only that the scene was broadcasted live in slow motion. Just how the heck is that possible?
Episode 24 has X-eins claiming his heart was betrayed.
Then aliens just a minute before the series ends. What are they? What do they want? Who knows? And it really doesn't help that they look like they're made out of lemon-lime Jello.
While it's impossible to prove the writer are Pandering to the Base seeing the poll  after the finale is quite hilarious considering the most popular characters survived while the least were subject of a Kill Them All. Maybe it wasn't even intentional but makes it weird.
While most likely unintentional, the name Liselotte becomes this to Scandinavian viewers. The name itself was a fairly standard name before World War II, but nowadays, it's replaced by "Lise" or "Lotte". The sheer unexpectedness of seeing the full name used in an sci-fi anime makes it unintentionally hilarious!