I've sometimes used the Mystery Box to try to get some of the newer items I've wanted. It's not too hard if you know the secret, but I'm not sure if I'm allowed to explain it here or not. It doesn't always work anyway.
When I wanted the new Urubu pet, but I didn't want to make my own but instead adopt and change an existing pet, I wated aaaages for the elixirs to be released (they took longer than usual), and then I waited for the Mystery Box to be the shop that sold them. I didn't have much luck the first time, but not too long later, it was that shop again, and I managed to get one.
I also managed to aqcuire some of the sock layer items when they were new, and some of the newer Atebus Shop items, and I recently got some of the new bird-related items (I still need that feeder with the grey squirrel though).
EDIT: So today they released some new grass ground items in Seedlings that I think will go well with the sliding scraps, we've been in need of more outdoor ground items that could go well with them, and the Mystery Box just happened to be Seedlings today so I've gotten 3 of them already!!! How lucky!!!