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.
Good parents who did what they had to do in order save Altair.
Despicable parents who deserved their deaths at the hands of Mykage for abandoning their own son.
Ass Pull/Shocking Swerve: Apollo from the first series and by extension Kagura/Amata, is revealed to be the reincarnation of Apollonius' dog that fell in love with Celiane. Not Apollonius. Really.
To be fair, it's not as if this couldn't have been the plan the whole time. The original series was very vague on this, and rewatching it, there's points where you see can see this more.
Word of God says they did plan it for the original series but the idea got scrapped halfway and they went with a straight Reincarnation Romance both in the original series and the later OVAs. So while the first half of the original series has some hints they stop halfway along and the matter is never mentioned again... which means that in context it isAss Pull.
Die for Our Ship: Mikono, from those who wanted badly to see Amata choose Zessica instead.
Amata himself also received a fair amount of this from the more rabid Mikono/Kagura fans.
Ensemble Darkhorse: Andy, MIX, Yunoha, and Sazanka are rather popular supporting characters. Even some of the less important background characters that aren't even named in-series have fanbases, such as the one female student who wears a bag over her head.
Ho Yay: Cayenne and Shrade get this in spades, which is surprising considering their screen time together (or lack thereof). They're rarely seen together but if they are it is either Shrade teasing and Cayenne reactingor Cayenne taking care of Shrade. It's one or the other, no exceptions.
Jerkass Woobie: Kagura. He's been treated and raised more like a attack dog than as a child by Mykage with a parent who knew about his existence but never did anything about it. Mikono was literally the only thing in his life he had to keep him going since he knows that there has to be someone who will care about him.
Moral Event Horizon: Mykage crossed it BIG TIME when he murdered Jin and he continues to cross as the series goes including killing Alicia, pulling a Grand Theft Me on Zessica, and mind controlling Kagura into killing his father Izumo.
Also, during the "Dating Mission" of episode 5 they are the only ones, I repeat, the only ones in a group with two guys and one girl. Who is that girl? Sazanka, a raging Yaoi Fangirl with a deep fixation on especially these two. Coincidence? I think not.
Ship-to-Ship Combat: As expected, the shippers are bitterly divided over whether Amata should end up with Mikono or Zessica, and whether Mikono will end up with Amata or Kagura.
Unintentionally Sympathetic: Mykage can be this for some people. He might have reasons to be angry at Fudo/Apollonius if you think that he got cheated on, Apollonius never apologized, in the OVA he unwillingly got an abortion, then he got lied again and gattai'ed with a dog. He has gone through something...
Villain Sue: Mykage. The only things he wasn't behind in this series is Ianthe sapping the life form the planet leading to its slow destruction and the curse of eve that lead to the extinction of the female gender. But he never cared about finding a solution to the gendercide problem either.
Zessica. Like Kagura, she's messed with, broken, and bodyjacked by Mykage and whenever she tries to do something good for Amata it only ends up with her suffering even more at Mykage's hands.
Shrade as well. He was born with a talent for music and, coincidentally, with powers to alter peoples emotions through it. Because of this he accidentally kills his parents, is then turned into a political weapon and made to kill dozens of people. Then he gets recruited but it turns out that he can do jack because his powers are too strong and would kill him. It goes so far that, by the time he gets introduce, he frankly doesn't care anymore. He gets better thanks to Cayenne and the others but he still dies.