Base-Breaking Character: Sohara is a big one for some of the fans due to her treatment of Tomoki. While some feel it's fair to keep his perverted (bordering on sexual assault) acts in check, others think she crosses the line and attacks him for things that aren't his fault, or are simply disproportional to the crime. It's worth noting that most of these opinions are from early on, before the insane level of Tomoki's perverted acts was revealed, and the hate is more of a Never Live It Down for blowing up his house.
Tomoki without a doubt. His latest awesome feat is when he disciplines Chaos for showing "love" to the kitten with a light smack to the head. In another episode, Tomoki (who is now Tomoko) is trapped in the girl's bathroom after a failed perversion attempt. Rather than go out and face the wrath of his friends, he flushes himself down the toilet.
It's definitely genetics in Tomoki's case. Tomoyo also shows some good Crazy Is Cool credentials. For instance, among her many pervesion attempts, this is her response when hearing from a crying Sohara about her son's Heroic BSoD.
Yoshitsune as well. His response upon witnessing the harsh treatment Sugata went through when he tried to visit his family?. This.
Ship-to-Ship Combat: Dear lord, not only is there no Official Couple, but also plenty of Ship Tease between Tomoki and his 4/5 girls, in other words, it's a shipping mine! Particularly vicious is the battle between Tomoki/Ikaros and Tomoki/Nymph shippers: While Ikaros generally had a more important role in the storyline than Nymph, and many readers/viewers consider her a Nice Girl and fairly attractive, not to mention her Undying Loyalty, she is also an Extreme Doormat, who still doesn't know, what love in particular means. Nymph on the other side is beneath her Jerkass and Tsundere tendencies also an extremly Nice Girl and unlike Ikaros, she really has The Woobie bonus going for her (and, by the way, quite some people think of her as kawaii). The Tomoki/Ikaros shippers have a tendency to swoon over Ikaros' hotness and absolute obedience and to call the Tomoki/Nymph shippers pedophiles (never mind the hypocrisy of calling someone disgusting when you like the idea of a girl who will do whatever her "master" commands, no matter what it is, without complaint), the latter ones on the other side usually point out Nymph's positive attributes. In comparison, the Tomoki/Sohara and Tomoki/Astraea Shippers are much more subtle and tolerant and often cool enough to laughingly point out that they favor a Darkhorse. Considering Hiyori Kazane's status as an Ensemble Dark Horse and the fact that she really is so much easier to pair off with the Protagonist, she was also a very popular runner, at least until she died.
Superlative Dubbing: The dub is very well made. All of the voices fit and the actors all do phenomenal jobs, especially Carli Mosier as Astraea, and the script contains countless woolseyisms.
They Wasted a Perfectly Good Character: Siren. Despite only appearing and dying in a span of one chapter, she actually had a neat character design compared to the other Angeloids seen in the story.
They Wasted a Perfectly Good Plot: It was highly expected that Oregano would be Sugata's angeloid, instead of what took place in chapter 52.
Nymph. She has the most scenes with Minos. One memorable scene has him, along with some of the other inhabitants, questioning why they made an "Electronic Warfare Model" if the "downers" haven't even found Synapse in thousands of years and whether or not they should just scrap it. This, all in front of Nymph, who is the model in question. If that isn't enough, then how about getting curb-stomped in every battle she's been in, one of which ended with her wings being torn off? Whenever the plot rolls, they like picking on her for some reason.
Chapter 47 turns CHAOS into this.
Chapters 69 and 70 further cements both Nymph and Chaos' Woobie status. Nymph starts lamenting that everytime she makes a friend, she ends up alone, remembering the bird that she was forced to crush and Tomoki going to Hiyori's house earlier that chapter. After Hiyori becomes flustered due to an Accidental Pervert moment shared with Tomoki, her powers go out of control and Nymph calms her down, and it ends with Hiyori wanting to be friends with Nymph, which she happily agrees to...Only to find Hiyori destroyed moments afterwards...Meaning it's another friend that she lost. On the other side of the coin, after chasing Hiyori and destroying her wing and Demeter, Chaos starts to cry once again and Hiyori realized how broken she is...and impales herself on Chaos' wings so she can realize that hurting people is wrong. When it finally dawns on her all of what she had done, she finally crosses the Despair Event Horizon and has a My God, What Have I Done?...And now Nymph's fully intent on killing her. Damn...
Woolseyism: The English dub contains countless, countless examples. The best example would probably have to be all of Astraea's dialogue, which overall makes her sound much, much more stupid than in the original Japanese, where she would say stupid things, but she wouldn't sound all that stupid saying them. The dub all around makes her both stupider and funnier. Compare:
Astraea (Japanese): "I came here, planning to eat all of [Tomoki's] food, but there's nothing inside this refrigerator. Why is that?! I'm so hungry!!"
Astraea (English): "I snuck in like a food ninja when nobody was looking so I could eat the yummies, but there isn't anything yummy inside this fridge, there's only me! God, why?!"
And it also takes away her ability to spell:
Astraea (Japanese): "How pitiful! How absolutely pitiful! I am Synapse's best close-quarters combat Angeloid, type Delta, Astraea."
. When it plays, you'll know that something awesome is going to happen.