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.
Anvilicious: In the manga only: Kana Ushiro, Jun Ushiro, and Yousuke Kirie each spend time lecturing the reader that people should care more about everyone else in the world, even if they aren't the "main characters" of a story.
Also in the manga: there are also Take Thats towards America along these lines; despite American characters rarely being depicted, characters in the manga show disgust for a perceived American selfishness whenever actions by the United States are mentioned.
Counterpart Comparison: There is some between Koyemshi and Kyubey, as both are small white creatures that trick children into making contracts with them that ultimately cost them their lives but are seen as preserving the universe. However, Kyubey takes a detached and emotionless perspective of humanity as a Starfish Alien while Koyemshi seems to actively enjoy the children's despair, and used to be human himself.
Designated Villain: Not exactly a villain, but America in the series is talked about like it might as well be a villain even though in both the manga and the anime, it never does anything antagonistic, or even does much of anything.
Family-Unfriendly Aesop: Kirie gets one from Misumi before his fight, as the first person to fight with the knowledge that by winning, he destroys someone else's universe. No matter what people say, everyone is not equal. Some people will always be more important to someone than everyone else, and when it comes time to decide between who lives and who doesn't, people will always choose the one who's more important to them.
And also it's impossible to live without taking life from someone else, be they animal, plant or human. Plenty have already died just to ensure your continued existence. Even Jesus and Buddha aren't exempt from this.
The epilogue for Chizu in the manga has the fairly family-friendly aesop that "Revenge is not an appropriate way to solve your problems, especially if it eneds up causing suffering to innocent people as a result". However, her family then refuses to press charges against Hatagai, essentially believing that they have no right to seek justice against him now that Chizu voided her own right by killing innocents for revenge, essentially sending the message that it's preferable to let a guilty man go than exact revenge yourself.
Harsher in Hindsight: As dark as Bokurano is, there's an example; when Ushiro accuses one of the pilots of getting cold feet, Misumi admonishes him, saying that "Everyone's scared." When you consider that she's his mother and is all but certain that her son is going to die, you can see that she's referring to herself and her comment has more weight.
Ho Yay: Ushiro and Kanji, in the manga. Ushiro even tells Kanji that Waku wasn't the only reason he stuck around despite not being in the contract, and Kanji realizes that it was for him.
There's a bit of Les Yay between Maki and Komo in the manga. Komo once comments, "I think your butt is a knock-out, Maki" in response to her new outfit, the two spend a lot of time together before Maki's battle, and when Maki dies, Komo is visibly devastated by it, even though it seemed as though the pilots had gotten used to their members dying after Kodama's death.
Jerkass Woobie: Jun treats Kana terribly and is (initially) one of the colder and less empathetic characters, but he has been through quite a bit, to the point where in the manga, Kana puts up with the abuse for his sake.
Kako doesn't take his impending death very admirably, including even trying to rape Chizu at one point, and he ultimately dies without fighting. Still, his experience is hardly pleasant, especially considering he's the first pilot after The Reveal in the anime, and even Ushiro feels sorry for him in the anime.
Ushiro: (getting ready for his battle) I bet Kako wanted more time, too...
Moral Event Horizon: Mr Hatagai goes straight over this with what he does to poor Chizu in the manga. So much that he had to be seriously toned down in the anime.
Koyemshi threatening to kill Ushiro to force Kana to join the game. Fortunately, Jun himself out-gambits him with the help of Youko.
As sympathetic as she is, Chizu firing Zearth's lasers at her rapists, and killing many innocent people by collateral damage in the manga can be seen as this. Her family acknowledges what happened to her, but even they consider what she did to be quite terrible.
Spell my name without a space The title is one word, despite the particle "no" being a separate word preceded by a space in essentially every other Romanization of Japanese.
The Woobie: All the main characters get this at one point or another. It's a Mohiro Kitoh series, what would you expect?
Of the side characters. Mrs. Komoda stands out, especially considering that she loses her husband and her daughter in rapid succession. Also Mr. Ushiro in the manga he loses his entire family and is seen as horribly depressed in chapter 64, until his students appear to try and cheer him up
Woolseyism: The official English translation of the manga explains the name "Zearth" as a case of Xtreme Kool Letterz rather than delving into a lengthy explanation of the mechanics of the Japanese language that can put a "z" at the start of "The Earth."