The anime teaches us that "Men" is a head cut and "Dou" is a torso blow. And in the title opening, Tamaki yells "Dou" while cutting at our head.
This troper, a kendoka in his own right, believes that Tamaki yells "Tou" rather than "Dou" while she strikes for the "Men" strike. "Yaah" and "Tou" are common shouts during drills. They do sound very similar though.
Reinforced in the dub, where Tamaki yells "YAAAH!" instead.
Tama-chan busts out some Fridge Logic at the end of an episode when she points out the legality of using two-sword style in High School.
In some of the later episodes of the anime, there's an arc where Toyama beats someone up over beating him in an arcade game, which threatens the entire team with being shut down as punishment, since he never officially quit, just simply stopped showing up for club activities. This led to much angst for team captain Kirino, fearing that she would have to lie about him having resigned to save the team. What bugs me is, why couldn't she have made his non-membership official by just kicking him off the team for the incident? By doing that, not only would Toyama no longer be on the official roster, Kirino would not have to lie about anything. Everything worked itself out in the end without her having to do any lying, but why did kicking him off the team never occur to her?
I think it had to do with her pride as captain and love for kendo. She wanted Toyama to enjoy the sport as well, and hated the idea of denying anyone that.
Also, in Japan, clubs tend to be a lot more 'serious business' than in the States. Kicking him out, especially as a student rather than via the teacher, may be seened as reflecting on the club itself rather than just the student. Hard to say though.
Makoto and Shinobu join the kendo club because their parents don't want their older brothers' kendo gear to go to waste. It makes sense for Makoto since he and his brother are both male and of similar build. But there's no way Shinobu with her height and size will be able to use most of Toyama's gear, i.e. her parents are just going to incur an additional expense buying all her stuff afresh.
We aren't told how the final tournament in the show ended. Tama-chan must have won the girls' individual tournamet, but how did Yuuji-kun fare? Maybe manga readers can answer?
The anime deviates from the manga after Tamaki's fight with Konishi. Otherwise, I assumed that Yuji and Tamaki did win.