In the game, you can unlock 2 sets of the "Special" Wallpapers and the last and final Box for the Pokemon Storage System after clearing the Delta Episode.

Unlockable	How to unlock
Box 31	Complete the Delta Episode
Special 1 (Hoenn Starters)	Complete the Delta Episode.
Special 2 (Primal Groudon)	Complete the Delta Episode.
Special 3 (Primal Kyogre)	Complete the Delta Episode.
Special 4 (Mega Rayquaza)	Complete the Delta Episode.
Special 5 (Team Magma)	Complete the Delta Episode.
Special 6 (Team Aqua)	Complete the Delta Episode.
Special 7 (Hoenn Map/Secret Bases)	Complete the Delta Episode.
Special 8 (Contest Spectacular)	Complete the Delta Episode.