Seasons- These were cool, not that I particularly liked them.
Pokemon Following- I might be the only person in the world who hated this feature. I don't think it's worth the resources and time to program in walking animations and sprites for all the Pokemon, when I never even talked to them. Shiny Leaves were like my only incentive.
Contests- Meh. Just for completionist sake I did them, not that I actually enjoyed them much.
Puddles- The more ways to encounter Pokemon, the more diverse designs can be implemented, so puddles are nice (STUNFISK)
Fog- NO.
Trainer Customization- This was great for the PSS, and I think they should bring it back. That being said, allowing us to actually wear our sunglasses would be a nice addition.
Underground Mining- This would be nice if you could mine anywhere. The DPP system of magically finding some walls that could be mined was tedious, but mining itself was fine. I like the Reborn version where you don't get worthless orbs, though.
Secret Bases- Cool touch-up in ORAS, although I only really use it to fight L.100 Blissey's at this point.
Rebattleable Gym Leaders- This was really cool, and I wish it could be implemented again, although make it once a day or something instead of the call feature from HGSS.
Battle Frontier- Bring this back!!!! I had so much fun in especially the Battle Factory, just cruising through. The Battle Maison can only be fun up to a point.
Rebattleable Regular Trainers/VS SEEKER- I'm adding this on my own, because every game since DPP didn't have this feature done well, in my opinion. I love being able to grind against trainers instead of Pokemon, and if the only battles I can do are with a sporadic phone call feature or only daily, then I can't do that well. I think a VS Seeker would be nice. Just like FRLG, some trainers don't even really need updated teams.