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.
YMMV: Black Cat
Adaptation Expansion: At the cost of cutting out certain aspects of the manga plot, the anime added an entire arc towards the end of its run that sought to tie together the significance of Eve's origins and the work Dr. Tearju did, along with providing some background on The Doctor. Add to that several of the Chrono Numbers who appear in the anime only and it's kind of sad that they had to sacrifice much of the manga's character development. It truly could have been awesome.
On the other hand, Train and Saya's relationship was much more developed in the anime, making Train's motivation more moving.
Angst? What Angst?: Train in the later half of the manga. He gets shot by a bullet that is known to transform people into monsters, yet just shrugs it off (despite everyone else including the Big Bad panicking). When he turns into a kid, his first thoughts are that it'll make meals and bus tickets cheaper. When asked if he's concerned that Creed is trying to bring about the End of the World as We Know It, he answers no, and that he's mainly concerned with what's for lunch.
Compressed Adaptation: The anime, which removes whole arcs, completely rearranges the whole start of the series, and cuts a lot of character development for everyone but Train and Eve, or distilled in a very awkward way. Which is strange considering that the anime is also an example of Adaptation Expansion.
Complete Monster: The Doctor is more twisted than Creed and doesn't have the excuse of being clearly insane. Pick one of his experiments at random, just one of them, and you'll likely agree that it's enough to warrant the most cruel and unusual death available. He even tells Eve at one point while trying to vivisect her that empathy is a truly pointless emotion.
Tendencies? The man has exactly zero qualms about killing you if you "stand between me and Train." Given his obvious propensity for seeing things obsessively... does anyone here have a mathematical formula for how long it would take for Creed to end up killing the entire world's population out of jealousy?
Also Shaolee, who spends his time deceiving people, is actually one of the cruelest Numbers and is quite creepy when you think about it, but looks just so pretty.
Evil Is Sexy: Echidna, although she oddly never makes use of it.
Fashion Victim Villain: Nice jumpsuit, Creed. Did it come with the open chest, or did you cut it out yourself?
Foe Yay / Ho Yay - The romantic / sexual tension between Creed and Train. Though it's rather one-sided, as Train clearly has zero intention of returning Creed's affections.
Creed murders Saya simply for the humanizing influence she has on Train. And after suffering a nasty injury that might have made people sympathize with him, he then tries to turn Sven into a mindless monster.
When facing down Sven, Torneo is all ready to use a nanotech drug on Eve to force her to become a mindless killing machine. Train shoots it out of his hand to stop him.
Strawman Has a Point: Baldor isn't always wrong. In particular, his attitude towards dealing with Kyoko is pretty justified given her previous behaviour. We're supposed to cheer for Train, who manages to miraculously reform her through The Power of Friendship / The Power of Love, but it's really hard to disagree with Baldor's "just kill her" attitude given all the deaths she's been responsible for up until to point.
An even more telling example is when one of Creed's Mooksblows himself up when Eve tries to help him, right after Baldor talked about how mercy is useless. Who's the Strawman again?
Unfortunate Implications: The only obviously gay or bisexual character in this series is The Big Bad, something that can be easily taken the wrong way. That said, there are a few upsides to Creed' portrayal: he nicely subverts the "gay men are wimps" stereotype despite being extremelycampy, is not a pedophile (he and Train are actually around the same age, Creed actually being younger than Train by a few months), and in his own warped way, is very loyal to the person he's interested in. He's depraved in the sense of "gay and evil", not "evil because he's gay."
As an aside, it's also worth noting that his love for Train is actually one of his only redeeming qualities. The only time he ever cries is actually over Train, and the only possibility of a Heel Face Turn for him was because of his admiration and weighing of Train's words.