Visit each location every day. If you find Nodame in her mongoose suit every day, at the end of the game you can play as a 3D version of the mongoose as well as unlock a mongooses and snakes mini-game.
Secret Level
In order to play a secret level, complete the game and see all the credits (which take a while). After their end, wait until "The End..." vanishes and you'll gain access to that level, where you play as an hidden character.