Trick Master, Contests, Secret Bases, Spinda, Battle Frontier, RSE had a lot of great things added to it that would be amazing to see just returning to the game. Personally I want to see those double battles which can be single battles like they did in Emerald, those where if you meet two adjacent trainers' eyes at the same time you'll get a double battle instead of two single battles.
But I'm mostly looking forward to Battle Frontier personally. I never actually got that far in Emerald and I loved the one in Pt/HG/SS so I'd like to see a proper Emerald Battle Frontier make a comeback.