Foe Yay: Kohei Kakihara is obsessed with Twenty Faces to the point, where he changes his appearance to look exactly like him and later tries to take Chiko under his wing. His main goal is to obtain Twenty's legacy, as he feels it was stolen from him a long time ago by Twenty himself.
Moe: Heavily and quickly subverted, as Chiko is by no means defenseless or in need of protecting despite initial appearances, and she isn't naive or innocent at all since she's had to deal with her parents dying and her only living relatives attempting to assassinate her for money. To quote from elsewhere: "If there were an absolute antithesis of moe, something that would completely convert to energy if it came into contact with moe, it would be Daughter Of Twenty Faces... the first two episodes might come across as a little moeee~ since Chiko is weak and vulnerable and tends to faint when attempting anything really strenuous and even picks up a nii-san really quickly. Then episodes 3, 4 and beyond happen and MATTER BECOMES ENERGY."
As a subset, Zettai Ryouiki is also subverted as, promotional image aside, the female characters all wear skirts that are absolutely no less than knee length and the animation even goes out of its way to avoid showing too much upper leg. Truth in Television for the era the show is meant to be set in.
As another subset, there is possibly a little bit of woobieism attached to Chiko ( especially in light of episode six), but she generally possesses such a "take charge" attitude about her life and circumstances that she doesn't really seem like she needs much comforting. On the other hand, pretty much anyone needs a hug after watching their dream life torn to shreds and then set on fire.
The Scrappy: The white-haired woman, who, while effectively evil, fast became intensely annoying in the way she went about things. Slightly confusing/poor characterization didn't help either.
Shunka turned into a bit of a Scrappy for some viewers; she seems to have most of the negative aspects of an Ojou without many of the positive aspects, and she's nowhere near as competent in practical matters as Chiko to boot.
What an Idiot: When a kid wants to enter your vulnerable submarine, of course you don't have to frisk her or thoroughly check what she's carrying in her basket. Even when she accompanies known crooks. Sure.