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.
Hoshijiro Shizuka's Image Song, "My Life". A Tearjerker about her final moments and stating she will love Nagate even as Benisuzume.
Broken Base: The CG Anime treatment has been held-up as having both impressive action sequences and atmosphere, as well as deplorable character models and awkward animation at times.
On the other hand, it can be argued that the anime flows better than the early manga, as (with the benefit of hindsight) it tweaks the timeline so that e.g. Yuhata is introduced earlier and Kunato humanized a bit (without diminishing what an asshole he is).
Cargo Ship: Nagate/Onigiri (or other kinds of food in general) is a common joke pairing.
Despair Event Horizon: Kunato after Nagate saves Sidonia from the planetoid Gauna. In his mind, he is a failure because a lesser pilot saved the day and will be celebrated as a hero, and because his actions resulted in more pilots dying than civilians being saved, he also regards himself as a murderer. When Tanikaze tells him that, while he'll never forgive him, he wants even Norio to be happy in Sidonia, Kunato cannot summon the courage to speak to him and instead runs back into his home and openly weeps. He's one of the very few characters in fiction to both cross the "forever evil" and "forever hopeless" event horizons.
Freud Was Right: The Guana's preferred method of attack is to jam their tentacles into the Guardians to penetrate the cockpit
Tsumugi's tentacle. It may behave like a young girl, but it resembles nothing more then a massive penis.
Les Yay: Izana and Yuhata have been getting an increasing number of moments with Nagate and Tsumugi growing closer.
Moral Event Horizon: Kunato purposely sabotaging a mission just so that Tanikaze looks incompetent for incredibly petty reasons is bad enough. But doing so gets Hoshijiro Shizuka killed and Honoka En placed in a coma. He never seems to feel any guilt over this. Having said that, in the anime his encounter with the Benisuzume leaves him quite visibly shaken.
Nightmare Fuel: To prevent a Gauna from reaching Sidonia, Kobayashi is forced to order an emergency acceleration. The arificial gravity system become unable to compensate for the acceleration, causing the residential blocks to crumble and many to die falling to their deaths. The scene is all the more horrifying in the anime.
Ugly Cute: Tsumugi's tentacle-head-thing. Tsumugi herself also qualifies.