One that comes to mind are Secret Bases. Make more areas for Secret Bases, and more customization inside your Secret Base.
In RSE, mixing records was pretty important. In addition to populating your game world with other people's Secret Bases, it controlled several other things. This time, rather than Mixing Records, simply do it automatically over Local Wireless. Just walking by someone with playing the game should be enough to "trade" Secret Bases, TV programs, and records. Similarly, interacting with someone over Wi-fi should do the same thing.
Give the Desert Underpass more of a purpose. It can still be a trainer-less dead end, but do something with it. Maybe if you come there with Regirock, Regice, and Registeel, it'll open a passage and reveal Regigigas?
Change the specifics of the Regi puzzles. Don't change how they work - obscure braille directions - but change what they ask you to do. Emerald did this too, for the record.
Kind of a given, but change / update the Gym Puzzles. Lavaridge, Mossdeep, and Petalburg Gyms are very good and memorable, and don't really need to change, but otherwise, fair game.
Combine the PokeCenter and PokeMarts, like newer games. But actually replace the Marts with something interesting, not just a house populated by useless NPCs.
Take Emerald's cue for alternating teaming up with Team Magma and Aqua. Also, let the teams keep their Emerald hideouts. But, have only one of the teams succeed in releasing their Legendary (Team Magma / Groudon in Omega Ruby, Team Aqua / Kyogre in Alpha Sapphire), with the other giving up on their search when they see the calamity caused by releasing said Legendary.
Include the Battle Tents, again moving all Contests to Lilycove. Include Mirage Tower as well.
Include places for the location-based Evolutions. New Mauville should have a magnetic field for evolving Magneton and Nosepass, Petalburg Woods should have a Moss Rock, and the Shoal Cave Basement should have an Ice Rock.
Desert Underpass and the expanded Safari Zone should be available as soon as you get to the area, instead of being barred off until after the National Pokedex.
To accommodate the above two, slightly expand the Hoenn Dex. First off, include Probopass and Magnezone. Secondly, include the non Hoenn-dex Pokemon available in Emerald. Specifically, the Safari Zone expansion has Hoothoot, Ledyba, Aipom, Sunkern, Pineco, Teddiursa, Houndour, Miltank, Shuckle, Spinarak, Mareep, Gligar, Snubbull, Stantler, Wooper, and Remoraid. Desert Underpass has Ditto.
All of those listed above should be included in the New Hoenn Pokedex. Their evolutions (including Ambipom, but excluding Gliscor) should also obviously be included.
Reintroduce the Altering Cave. However, change its mechanics and the available Pokemon. Instead, make the starting Pokemon depend on country (or something similar). Interacting with people of other countries will add their Pokemon to your Altering Cave, and add yours to theirs. There should be around twenty or thirty different Pokemon available. Keep it exclusive to post-National dex.
Don't bother adding new Megas. Honestly - there's nothing that makes Mega Evolutions preferable to a Form Change, and, Mega Evolutions, unlike Form Changes, would involve patching XY, which would be a pretty stupid decision considering ORAS and XY were in development at the same time.
Don't worry about explaining the existence of Fairy-types. More or less, they should just ignore them - much like how FRLG treated Steel-types (and the Dark-type moves).
Include and expand the Battle Frontier.
I would love it if they'd implemented a feature that would save your game automatically, haha. We always save before quitting, but sometimes, though, we wind up forgetting and lose a lot of progress; these kind of moments could be very frustrating. We are human, so we're all bound to make mistakes like this. If they'd added some auto-save functionality, these things would never bother us anymore. Was hoping for this to make it into X and Y, but unfortunately, it never happened.
Please no. Personally, I hate auto-saving games. I like being in control of saving, because then you don't have to worry about whether you just bought the wrong super-expensive item, blowing all your money, or deleted an important move with no easy way to get it back, or wasted way too many Poke Balls for a catch to be worth it. With auto-saving, you'll never know if such mistakes will be permanent.
Just don't turn off your 3DS. Close it and put it on Sleep Mode. I save occasionally, but I almost never turn my system off while playing through a game. Less chances to lose progress.