Awesome Music: The anime's opening, "Sidonia". Also an Earworm. Special props go to the second opening.
Hoshijiro Shizuka's Image Song, "My Life". A Tearjerker about her final moments and stating she will love Nagate even as the Crimson Hawk Moth.
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.
Ending Aversion: A lot of readers hated the ending; mainly due to how rushed and abrupt it looked with the time skips, how the characters were officially paired together and some storylines remaining unresolved.
Fan-Preferred Couple: Majority of the fans prefer that Nagate should ended up with Izana which is exemplified in the anime where they gave a huge focus on their relationship. However, the ending shows Nagate ending up with Tsumugi instead whose consciousness was uploaded into the clone body of her "mother", Hoshijiro, and they have a daughter together which didn't sit well to Nagate/Izana fans.
Les Yay: Izana and Yuhata have been getting an increasing number of moments with Nagate and Tsumugi growing closer.
Subverted when Yuhata turns herself into a male.
Moral Event Horizon: Kunato, in the anime, deliberately strikes Hoshijro Shizuka for no reason at one of the food services locations, and when Nagate calls him out on it, promptly turns and breaks Nagate's arm, all because he's jealous that Nagate is flying the Guarde relic that his family owned, something Nagate had no choice in. 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.
Ship-to-Ship Combat: There would be Nagate/Tsumugi and Nagate/Izana. The ending itself pulled a full-blown war when Nagate got together with Tsumugi and had a kid while Izana is paired with Yuhata, who changed her gender into male.
Ugly Cute: Tsumugi's tentacle-head-thing. Tsumugi herself also qualifies.