Also known by its original name of Neko-neko Nihonshi, the cat thing is a delight. Although, truth to be told, I'm not entirely sure about some of the characters, most are quite recognizeable. Shinsegumi commanders, for example, or Ryoma Saotome. The episode of Sei Shounagon is my most favourite, with the narrative of her breaking with the establishment told to perfection (I have never read The Pillow Book, mind).
The OP and ED from the 1st season were phenomenal.