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 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).
Also, many were disappointed that this manga was adapted to an anime, most Nihei fans wanted a true Blame! anime or at least, Biomega.
Cargo Ship: Nagate/Onigiri (or other kinds of food in general) is a common joke pairing.
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.
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, which features distant indistinct blood splatterslike bugs hitting a car windshield...
Ugly Cute: Tsumugi's tentacle-head-thing. Tsumugi herself also qualifies.