I haven't played anything newer than gen 3, so bear with me if some of these things have already been done.
I'd really like to see some quality of life improvements, similar to what was done from R/S -> FR/LG. That means things like being able to bandbox multiple pokemon to move them around in the PC, being able to give/take items without having to move them into your team, and having more (functional!) sorting and marking methods.
Other QoL improvements:
-Marking pokemon with 1-4 different symbols is nice, but I'd love to be able to tag my pokemon with some text and then search/sort by tag.
--Having longer names for boxes would be great, too.
-Being able to define some pre-made teams, then swap to that active team with just one or two clicks, rather than having to depost and sort 6.
-an improved help system. FRLG's was okay, but it was so vague and shallow. Having a help system with databases of type matchups, game mechanics, where different special NPCs are located (tutors, haircuts, etc), schedules, etc would be very handy when I don't have internet access.
--being able to access it while in battle would be great.
-some form of reminder or obvious indication of how using an item or switching pokemon is going to affect turn order/ speed.
--also reminders for how many de/buff stacks I have, and how those are affecting my stats.
-some obvious way to see how my badges have affected my stats.
-having the pokedex store my last cursor location. This is the most frustrating thing in FRLG while trying to find the legendary dogs.
--a return to the RSE dex searching system, where I can find pokemon by type/ alpha/ number/ size/ etc, rather than "grassland" or "savannah".
-some method of leaving notes for myself, such as what IVs a pokemon has, or which two are my breeding pair, which ones I want to keep at level 50 for the battle tower, or what I plan to do next in-game in case I don't play for a few weeks and forget.
-a way to stop pokemon from accumulating experience (and also evolving) that's not a held item.
-backwards compatibility, even if it has to be like GSC -> RBY with a time capsule.
-having multiple save files without external hardware.
-a system to rebattle that's not convoluted and frustrating (PokeNav) or a hassle (VS Seeker)
-more bindable hotkeys
--I want to be able to have bike on left bumper, FLY on right bumper, and dex on select.
-allow me to change the in-game clock. Sometimes people move.
Personal preferences:
-more towns that don't have gyms, just places you can go that are fun to hang out in
--they don't even need to be on the linear path you take to the gym cities[/indent]
-NPCs with a little more personality
--maybe if they even had something as simple as schedules they follow per day of the week, like Daisy or the haircut brothers in GSC?
-satisfying OPTIONAL fishing minigame
--sometimes I want to relax and fish, and other times I just want to get on with EV training. I'd like to be able to choose.
-Game Corner (I heard that it's been removed? That's no fun. It's a pokemon staple.)
--if they bring it back, then the ability to buy more than 500 coins at once (perhaps a variable number, just like every pokemart), and the ability to cash out your coins.
-gym leaders whose pokemon scale to match the level of your team
-the return of PokeGear and those calls from trainers who just want to chat you up
-more water routes and more interesting/ diverse water-types
--please, no more fish pokemon
---actually, yes, more fish pokemon, but add like 100 more and make their size/ length/ fin type/ scale type relevant (maybe an attack based on size, kind of like Waterspout or Low Kick?), and add every fish pokemon from every old game
----no more tentacools, please, just make it go away
-no more new evolutions/ baby versions of old pokemon. They make no sense. Maybe Eevee is an exception.
-bring back low-encounter rate pokemon of very high level in some areas, like the level 45 tentacruel and 29 dugtrio in RBY.
-graphics that stand up better to time, like the cartoony ones of GSC/RSE. FRLG tried to make everything look higher-def, but the pixellation really takes away from that. RSE embraced the pixellation, building on the great look of GSC but with enough detail for pokemon designs to be easier to see.
-GSC battle interface. The name/health/level block in all the games afterwards is way too big. GSC's was small, elegant, and effective.
-less grind. If I'm going to be doing something like battle tower, why can't my pokemon just all be temporarily raised to level 50/100, pokemon stadium-style?
-monster ranching. Being able to design my own area where pokemon roam, train, and breed.
-fewer pokemon based on objects with high mechanical complexity or whose form is a result of being designed for humans. Pokemon have no need for washing machines, so it doesn't make sense that they would evolve into them, nor does it makes sense for a washing machine to somehow be the result of a series of mutations. A sword or magnet or sphere or something, sure I guess.
-less focus on evil teams and world-shattering events. Team Rocket was more of a side thing in RBY+GSC, and their goals were somewhat believable (even if they were terrible at accomplishing them). Team Magma/Aqua makes absolutely no sense, and it makes doubly less sense that a 10-year-old is tasked to save the world in any of the games (or even given the trust/ rare items of adults that have literally just met the kid). There's a perfectly good league champion right there, and maybe even some police or a government *gasp*.
-continued inclusion of nonstandard communication. It's nice to remember that some folks depend on ASL/sign or braille. It would be nice if there could be some colour-based or sound-based puzzles as well.
-no more funky 2v2/ 3v3/ XvX battle modes. Sure, a mode where you have to have a certain type, or a certain level, or a certain tier is fine. But what's the point of fighting with 3+ or in a battle royale? At that point it's no longer about skill, and just about speed and AI/ luck. 2v2, maybe if the damage/health scaling were changed so that pokemon don't get KO'd in one or two hits, so that it actually matters which two you've chosen. Otherwise it's silly.
-more individual variety among pokemon. Pokemon like Spinda make sense, because they're all similar, but a little different, just like real animals. It's difficult for me to comprehend how a mew can change its species to become a gyrados, but I can see how a spinda might eventually become a teddiursa or something. It's already been done in both the anime (eg ash's pikachu vs ricky's sparky) and the games (RB vs Y koffing) anyway.
--along the same lines, either have no shiny pokemon, or a whole lot of different "shiny" variants of the same one.
-getting away from a m/f gender binary. There's plenty of other gender schemes in biology, and plenty of other methods of reproduction.
-remove explosion and selfdestruct. Why? Just why?
-more interactive pokemon like Castform. Even if it was terrible, castform both matched the theme of RSE perfectly, and also made battles more spontaneous and interactive. As is, battles have very little interaction beyond debuffs, roar, and spikes. Being able to have your team change as a result of extant conditions or the actions of the enemy goes a long way to making it more interesting, like Magic the Gathering.
--this could extend to pokemon like Remoraid, Shellder, or Paras, which have so much unused potential, or moves like Secret Power.
-no more time- or place-exclusive features. I'm so frustrated that I can never get Jirachi, Ho-oh, Lugia, Deoxys, or get a Latias with Soul Dew. Sure, it's a single-player game, so it shouldn't matter, but it's not actually. As soon as Gamefreak introduced anti-"cheating" code, they needed to stop making unobtainable things.
-New game plus mode, where you can pick your starter from any pokemon in the game, and the dex is already filled in. I'm tired of having to to use an emulator/ gameshark in order to start with a sandshrew or eevee or pikachu or something like the trainers in the show do.