I also missed secret bases from RSE. Mine was in a tree in the middle of a lake. ^_^ Totally awesome.
I liked the Underground but it felt too huge and grindy. There was too much space and not enough rewards; I liked when I got an item, plate, fossil, etc. but the Orb currency system was annoying. The capture-the-flag system was insane grindy as well.
The VS Seeker definitely needs to come back. HG/SS had such a dearth of exp without it, my pokemon could barely make it to level 40 just fighting trainers normally before the elite four.
I'd like to see a way to import or trade items similar to pokemon. I did my best with hold items and trading pokemon over when I was consolidating all my pokemon onto my SS cart, but all my sacked and gutted GBA games still have a lot of TMs and rare items on them. I was also really sad about leaving my killer secret base behind in Sapphire.
I had the glass pidgeot statue for doing really well at contests. I wish those items could have been imported into Gen 4 somehow. A lot of the secret base items in Gen 4 are pretty ugly imo.
I agree that there should be a way to just numerically see what EVs and IVs a pokemon has, no more of this messing around with phrases and trying to guess with the EV berries and stuff.