Base Breaker: 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.
Complete Monster: Minos, the master of Synapse, refers to humans as "downers" and "bugs". He also beats Nymph whenever she fails her orders (or when he feels like it) and constantly threatens to destroy her. It's likely that he also treats the other angeloids that way, threatening destruction if they don't provide entertainment for him. This "entertainment" includes such things as ordering Ikaros to annihilate the Tower of Babylon and the surrounding city, which would kill countless people, and placing a bomb around Nymph's neck, triggered to explode if she again failed to bring Ikaros back to Synapse. The worst personal and petty thing he did was probably the time he ordered Nymph to call on her pet bird and prove her loyalty to him by crushing it to death. After she did so, he stomped her face into the ground while laughing about how "That was pretty fun. I'll save scrapping you until next time." Nymph goes on to thank him for not destroying her, which in all those cases, can easily be interpreted as "Thank you for not destroying me today." He does all this while smiling evilly the entire time, and does these sorts of things after the series fully establishes that the angeloids have feelings and emotions despite their artificial natures. Both of the angeloids in question cry their hearts out after recalling what they were ordered to do. The sections that have him in it are when the plot shows its dark and serious side.
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 Awesome 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.
The Scrappy: Mikako is widely seen as the worst character in the series because she has no purpose other than to goad Tomoki into misery for her own enjoyment. Her whole shtick of "Organize an event, rope Tomoki in and then humiliate him" was funny the first time, chuckle-worthy a second time, facepalm inducing the third time and rage inducing every time after that.
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 Lolicons/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 Darkhorse 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.
Uncanny Valley: The anime has one when [[spoiler:Chaos impersonates Tomoki. At this point, the only expression Chaos has is her Glasgow Grin, and her eyes are constantly adorned with three lines of light akin to Ikaros or Nymph when scanning. This expression on Tomoki's face is horrifying.
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."
Astraea (English): "Look at me! This is sad with a capital 'C.' I'm The Synapse's bestest Angeloid in In-Your-Face combat! I'm Astraea, a Delta type, even!"