Dude, Not Funny!: Various scenes and YMMV, but the Valentine's day special where Kaworu attempts to rape Shinji in a park stands out. Also, the jokes about Gendou's hormonal problem and tendency to look like a child molester. We also suggest you don't think too much about the implications of Naoko's reappearance.
Fridge Horror: Gendou's fanboying over Shinji seems to parody the daughter complex in comedy mangas, and no one wants to remember this element of his original characterization in the context of a high school comedy (also, it offers a scary new explanation for why he thought in The End of Evangelion that he'd be a danger to Shinji if he raised him. The jokes about Shinji being a mama's boy. Ritsuko's occupation as the school nurse, when you consider that she acted as the school director with Touji in the original series and manga. This manga also sheds light on Naoko Akagi's special brand of mental illness, Ritsuko's obsession with the Ikaris and Kyouko's lack of parenting skills. Thank you, Raising Project.)
There's also the possibility that Yui participated in creating Rei.
On a lighter note, how does Gendou know how it feels to wear the shiny girly swimming suits?
Asuka's clumsy fights with Kaworu over Shinji, and the scene where she calls him a homo and he shrugs in absolute disdain. Yui in a baseball outfit, especially since she is in command all the time and was spared the fitness bike silliness.
Heartwarming Moments: Many of Shinji and Rei's interactions with Yui. The scene where Shinji is sick in bed and tended to by Rei; his reciprocation when she gets sick in a recent chapter. Shinji's multiple rescues of Rei in virtual realities during synchro tests. Shinji's moments with Asuka usually involve a scene on the beach and a reminiscence from their childhood but are generally followed by an Accidental Pervert + Megaton Punch incident. The scene where she eventually kisses Shinji was very fluffy, though. (When Shinji compliments part of Asuka's bento lunch, he thinks he offended her by not praising it enough, but when she walks away we see that she's SO HAPPY that he liked some of it!◊) Most of the ohanami episode, with the (short-lived feel-good "happy families" feel. Asuka's few encounters with Kyouko involve a rain of adorableness. Gendou's daydream about a grown-up scientist Shinji both qualifies as a Crowning Moment of Heartwarming and as a Crowning Moment of Funny. And let's face it, Yui embracing Gendou publicly (without Tanging him!) after his rescue of the MAGI system was surprisingly cute.
Asuka/Rei. If girls currently do not fall at Shinji, then usually fall at each other. Not to mention the many Shinji's dreams and title illustrations. They become even more friendly toward each other late in the series and sometimes they notice even some sort of attraction between them. In one extra chapter they have nearly full blown yuri scene when Rei is intoxicated by alcoholic odor. And now both girls reached even Accidental Kiss level.
Moe: The manga is like an inventory of Moe stereotypes and more; Shinji is just adorable.
Moment of Awesome: Whenever the situation looks hopeless, Gendou temporarily becomes incredibly competent and Kamina-level badass for a few pages and a Crowning Moment of Funny occurs. Shinji also saves the day a few times, but not as spectacularly.
MST3K Mantra: We suggest you only think about the original series and its correlations with this when it's funny.
No Yay: Gendou-Naoko. It's kind of like Shinji-Misato with wrinkles and an intolerable amount of deviousness.
Rescued from the Scrappy Heap - Gendo. To clarify, he's never been a scrappy in this series, but many fans didn't like him much. However, this series may as well be titled Neon Genesis: The Gendo Ikari Popularity Project for how much fans love this version of Gendo.
This Is Your Premise on Drugs: Strange and unrelated things are being made at the Centre for Artificial Evolution, such as Moe swimsuits and probably "special vitamins." What do you think Gendou derives his energy from? From Moe swimsuits and fitness bikes.
Unfortunate Implications: Both the manga and the game, have made fans, particularly Kawoshin shippers, uncomfortable due to the amounts of homophobia revolving around Kaworu that's played completely straight. Most infamously when he attempts to rape Shinji.
The Woobie: Rei is particularly fragile emotionally and seems to have gone through a lot of isolation.