If you paperize the area around a circle of flippable flowers, you will see a stickable area appear. Stick a sticker and a "?" block will appear. Inside the block will be a more powerful version of the sticker you originally stuck.
After beating the game (and watching the credits), the screen will shift to the book from the start of the game. The book closes and the light turns off. At this point, just wait about three minutes. A hidden lullaby song will start to play, and will continue to play until you hit a button.
In the background of certain levels, you can spot Mario's brother Luigi, who can be peeled off the level by Paperizing. If you peel him off in all 5 locations, he'll appear during the credits sequence. In addition, each individual peeling will unlock a rather amusing newspaper article in the leftmost house in Decalburg's Residential Area.
Megaflash Stickers are the rarest and most powerful battle stickers in the game, but each one will only ever appear in one set location, (except the Megaflash Hurlhammer, which appears in two) and some can be very tricky to find. However, once you know where to find one, you can get as many as you want, so it helps to know where they all are.
You can unlock the following exhibition rooms by completing the 2 sections of the museum collection: