Beauty Equals Goodness: Inverted and played straight. The Babyeaters are elegant crystalline things, yet they based their entire culture on the slow, painful consumption of their own sentient offspring. However, the even worse "Super-Happies" are utterly disturbing blobs of tentacle and colour.
Deliberate Values Dissonance: Future social mores aren't like present ones, much like present ones aren't like those of several hundred years in the past. A particular example is future humans' views on rape, which are so divorced from modern mores that the latter are incomprehensible to the protagonists even after being explained.
Eats Babies: Subverted and inverted by the Babyeaters — not only is the Eats Babies trope not used as a simple sign of being evil, but in the Babyeater fiction, letting too many babies live is used as a simple sign of being evil.
Esoteric Happy Ending: Deliberately invoked — either or both endings could be considered this, depending on your values. According to the author, the ending that involves killing billions of humans is the good one.
First Contact: A triangular example between Humans, Babyeaters, and Superhappies all at the same time. Justified by all three races having been attracted by an unusual cosmological phenomenon in the vicinity.
Gallows Humor: One of the main coping strategies of many characters in the last chapter.
Infodump: I've translated the aliens' language! But before telling you what they said, let me bring you up to speed on the history of statistical language-translation methods...
Intentional Engrish for Funny: The humans' translation software isn't perfect, but it gets better over time. Also, some ridiculous-sounding statements that the characters assume were garbled in translation were, in fact, translated correctly.
And, in one ending, "In The Future All Life Will Be One Race."
Just in Time: Deconstructed.They kill ten billion people because of the unknown risk that the aliens might otherwise show up in time, which there is little real basis to think would happen. Waiting six hours would have saved them. This is the correct decision. Some of the ships that are evacuating as many people as they can don't leave in time and get fried by the supernova.
The Baby Eaters use the same word for "to eat babies" and "to be moral". This makes it rather difficult for the humans to explain that they consider baby-eating not to be moral.
The Superhappies use the same word for "to talk" and "to have sex", because they think and communicate by exchanging genetic material, which means talking and having sex are literally the same act to them.
Multiple Endings: Including interactivity - the author announced at the split point that the true ending would be determined by whether anyone came up with the correct solution in the comments to the post before the critical update.
Not So Different: "They're a lot like our own children, really." That is, not only are the Babyeater children like human children, human children are like Superhappy children ... and the Superhappies feel as much revulsion for how humans treat their children as humans do for Babyeaters eating their children alive.
Older Than They Look: The humans have developed biotechnology which is implied to allow them to live forever.
Shout-Out: "The aliens will consider this one of their great historical works of literature, like Hamlet or Fate/stay night..." The Superhappies also have a ship officer with the rank "kiritsugu" which is the family name of a major character from Fate/Zero who had a background role in Fate/stay night.
Values Dissonance: In-Universe — the plot is "Future Humans" (as different from us as a typical alien race from more typical scifi) make first contact with two utterly alien species at the same time. Then the Human command crew spend twenty-four hours discussing Values Dissonance.