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.
Complete Monster: Gendo manages to skirt along the edges of this. See his actions at the bottom of the page: killing (indirectly) his daughter-in-law and grandchild to make Shinji follow (unwittingly) Gendo's plan. If it wasn't for his actions at the end of volume 4...
Crowning Music of Awesome: The entire soundtrack. Yes, there is a soundtrack to a doujinshi manga. However, special mention goes to "Girl" and "Holy Day". These can be heard either here for just the soundtrack, or here for select scenes included (all ages friendly, no adult content included). One is a playlist, the other is 4 part youtube clips.
Ending Fatigue: One of the "strikes" against the series. There are a few moments of, "Aw, that's a good ending...oh, wait, there's more."
Fanon Discontinuity: Fans of the work usually like to pretend that 1.5 doesn't exist since it's out of character smut. One reading the series can even just plain skip that chapter it won't affect their reading.
Iron Woobie: While Shinji was debatably this in the original series, he certainly fills out this role in this story. This is best exemplified when he goes off to fight the MP-Evas to save Tokyo-3, even though he knows it's essentially a suicide mission.
Jerkass Woobie: Ghost-Asuka is far more cruel and mean-spirited than she ever was in the main series, but that's hardly surprising considering what she went through.
Moral Event Horizon: See Gendo's actions above. Aside from that we also have SELEE's actions during the series take on the events of end, where like in the normal series, the virtually destroy Tokyo-3 and fully intend to murder everyone in NERV. Thankfully they don't get away with it this time.
Nightmare Fuel: A few sections stand out, most prominently is Rei's suicide and the "revenge" taken by Ghost-Asuka.
Rescued from the Scrappy Heap: Shinji becoming a Determinator to extreme levels as well as becoming much more heroic puts him in a much more favorable light in the fans view than in the main series.
Tear Jerker: The whole damn story. But especially Rei's suicide, the destruction of Unit 02 and Asuka ("This is Unit 02's self-destruct code. It has already been activated"), most of what Ghost-Asuka says in RE-TAKE 0 and 4, and finally Shinji leaving Asuka for Ghost-Asuka at the end of RE-TAKE 4 ("Yeah, but then, you'd always be alone").
The scene in the first volume in which Rei takes blue contact lenses and pours red dye all over herself in order to emulate Asuka is pretty heart-wrenching.