Things I would love in a Gen 3 remake:
-Keep EVERY feature XY has. Don't.cut.a.single.feature. (Seriously GameFreak, stop doing that in every release)
They'll want to rename Pokémon-Amie, but this applies in general.
-VS Seeker (I know RSE didn't have this but Gen 3 introduced it anyways)
Yup: just allow it through the Pokénav, and let it do for Gym Leaders and the rival(s) too.
-Keep all of the improvements Emerald had over R/S
I wonder how they're going to handle the three legendaries, but yeah.
-Secret Base WITH online
Basically render unto this what Masuda gave to trainer customization.
-Pokemon following you feature from HGSS
They've got other fish to fry.
What else? Hmmm...
Some ideas:
Vastly expand the Hoenn Contest system for compatibility with Amie + reduce the randomness and players' general inability to influence the outcome of matches; really, contests could be decided really early on, yet it takes a quarter of an hour to then finish the damn things.
Condense or shorten the water routes between Ever Grande and Pacifidlog, compensating for space by adding more (excuse me) depth to the diving portions. Mirage Island should earn some extra too, perhaps Latios/Latias/maybe Deoxys/whatever.
Add PWT features to the Battle Frontier, pls.
Designate a rival (either Wally or gender opposite) and friends a la X/Y; if possible, give Prof. Birch some actual involvement with the main game following early-game.
No Game Corner anymore, so something will have to replace the one in Mauvillea new mini-game, maybe?
Streamline biking system, either by using skates for Acro-accessible areas and adding gearshift to regular bike or by making it a multi-purpose mountain bike.
&c.