It's not necessary for game completion, but in order to get a lot of the extra scenes (the bunny house comes to mind) you need to go to the fourth city, in the north east corner; there's an elf that will synthesize items for you by combining other items. (It's the second option when you talk to her). The items you want to be making are in the 4th menu from the left when the shop dialogue shows up - you want to make sure you have at least one of everything she can make in that menu in order to access all scenes.
The easiest way to make sure you have all the items you need is to take a screenshot of the game, highlighting each item you want to make; that way, you can play match-the-pictures with the Japanese characters. You want to go to the fifth town (I think fifth, might be sixth) and near the entrance there will be a little market place with vendors that sell the materials you need.
Unfortunately, those vendors don't sell everything you need - in particular there's one item they don't sell that seems to be necessary for the bunny costume. It's the one with only two or three characters, and you need 2 of them for a piece of the bunny costume, and 5 of them for something else. Does anybody know where to find those items?