(The music is fantastic.)
The sticker setup seems to be just the one screen. There might possibly be some type of item you buy or obtain to increase how many 'pages' of stickers you can have (kind of like the different sized wallets you can buy in Ocarina of Time, for example.) It's looking like they may have it similar to the current format where you can hold up to 10 items at a time, but in this case, hold up to a certain amount of stickers with bigger ones obviously taking up more space and making you manage them better for the perfect array (sort of like Brawl's trophy sticker thing).
The only downside to this I'm seeing is what everyone's already mentioned: if your basic attacks are stickers, what happens if you're at a hard boss that requires endurance and good planning and suddenly run out of stickers? Also, it seems that it could slow the place down quite a bit by having to search every single square inch of the levels you visit for stickers, and you'll have to if the game is gonna be based off this system.