Shinsengumi's Inspector Yamazaki reported on the clash between Katsura's faction and Takasugi's faction to Vice-Commander Hijikata Toushirou. Hijikata wondered how Katsura's faction, with so few capable men, were able to fight off Takasugi's faction, which had heavyweight stalwarts like Kawakami Bansai 河上 万斉 and Okada Nizou 岡田 似蔵. Yamazaki replied that Katsura was assisted by Sakata Gintoki 坂田 銀時.
Hijikata explained (while wolfing down a bowl of 'Hijikata Special') that he ignored Gintoki in the past because there was nothing suspicious about his activities that relate to Joui activities then. Now as Gintoki was injured in the same fracas, a link is established, and Yamazaki was ordered to investigate Gintoki's relationship with Jouishishi, with the orders that Gintoki is to be killed if investigations proved that he is indeed a Joui rebel.
Thus Yamazaki decided to infiltrate the compound where Gintoki was recuperating, aka the Shimura dojo, Koudoukan 恒道館. Though his entry into the dojo was smooth, little does he know that leaving the compound would be fraught with danger ...
Yamazaki spouted 越前リョーマ Echizen Ryo-ma's catchphrase 'まだまだだね' mada mada da ne, meaning 'You still have some way to go'. His cap logo is a spoof of Ryo-ma's cap with a Y-like design in place of Ryo-ma's 'R', while for the logos on the shirts, Yamazaki's 'Y' is seen replacing the double 'Y' logo on Ryo-ma's shirt.
the students in blue and white shirts standing by the side are a reference to 青春学園中等部 Seishun Academy Secondary Department's characters, see image below:
the students on Musashi's side of the badminton court appears to reference 氷帝学園中等部 Hyotei Academy Secondary Department's characters, see image below:
the black cat is probably a stray, unlike カルピン karubin Carribean, owned by Ryo-ma's family, which is a Himalayan pedigree breed.
The poster on the wall outside the room states 'TV Champions, The King of Good-Guys Contest, Contestants'.
The character behind Otsuu is キシリア・ザビ Kycilia Zabi from Gundam. This contestant's entry is obviously ironical since this character is on the side of the 'bad-guys' in the Principality of Zeon in the Gundam series. The urn she is holding is the 北宋の壷 hokusou no go which can be found in the Gundam 0079 Card Builder arcade game.
JUMP manga read out by Kagura to Gintoki -
the first is a reference to Dragon Ball, with フリーザ Frieza being the character name referenced.
the second manga Kagura read out to Gintoki was 『いちご100%』 Strawberry 100%, with the characters Manaka Junpei 真中淳平 and Nishino Tsukasa 西野つかさ being referenced.