Base-Breaking Character: Chizuru is an ongoing source of disagreement and debate within the fandom. Many fans feel that she's too weak and passive a Player Character who spends too much of the game playing the role of Damsel in Distress, and that her demon powers provide her character with potential which is criminally underused. Others feel that her serving as emotional support to the Shinsengumi is an equally valid form of strength, pointing out that she's a very proactive woman by the standards of the time period and that a couple of years of sword training would hardly make her equal to the villains, almost all of whom are themselves demons or furies with years of extensive combat training.
Draco in Leather Pants: Kazama has a not-inconsiderable fangirl following, in spite of the looming threat of rape he represents in the common route and the fact that he's the main villain in Hijikata and Saito's routes and the cause of several bad ends in others.
Play the same game with Nagakura. Kyoto Winds gave him his own route too.
Sanan is no different, seeing as he now has his own route as well.
There are still plenty of fans who are unhappy about Shiranui not getting his own route.
Even Kaoru and Itou have their fair share of fans!
Ho Yay: Inevitable in a Cast Full of Pretty Boys; Okita's idolization of Kondou is a particularly notable example, and there's a lot of it between Saito and Hijikata in the drama CDs and other bonus material, to the point that Okita is able to bribe Saito to turn a blind eye to the fact that he's lost a uniform by giving him Hijikata's book of poetry (with some indications that he's used the medicine made by Hijikata's family as a similar bribe in the past).
Romantic Plot Tumor: Surprisingly averted in the anime, considering its Romance Game origin. Hijikata and Chizuru don't become an Official Couple until the second-to-last episode, and the plot just marches right on after that and kicks the romance aside. As a troper said before, "It's a romance anime without romance, how cool is that!".
The Woobie: Pretty much everyone in the show. This is a story about the Shinsengumi we're talking about after all.
Values Dissonance: Chizuru is frequently criticized for not fighting when, as a demon, she has physical potential greater than that of humans. However, the story takes place in Bakumatsu Period Japan, in a culture of very strict gender roles and social classes. In the context of the time period, that Chizuru dresses as a boy and carries a sword, travels to Kyoto alone in search of her father, hangs out with the Shinsengumi and occasionally takes a swing at the villains in a pinch would actually make her quite the tomboy.