Well, for starters, a Dark-type Gym is looong overdue. Game Freak seriously needs to bite the bullet and put one in already. =P
I think in terms of a new battle system, it should be tweaks to the current system. I'd like to see more focus on combo attacks beyond the Pledge moves in double/triple battles; they took the time to add these combo moves to the game, so I hope they spend more time on this concept.
Also, I really believe Water should be weak to Poison. First off, poison can contaminate water, so the change already makes sense. But Poison is such an underused attack type in PvP battles, and it's because it only has one type it can hit super-effectively; the only Poison moves you'll typically see are Toxic and Toxic Spikes; offensive Poison attacks are ignored. Water Pokemon are also quite a common sight, due to their versatility. I think this change could balance things out a bit more in the game.
Next, Ice needs to be better defensively; they're way too fragile. Ice Pokemon are hardly used in battle because of how many common attack types they're weak to. Also, they only resist themselves. The problem is that there's no good weakness to remove from Ice, since all the weaknesses (Fire, Fight, Rock, Steel) make sense, since fire melts ice and physical force can break ice. Perhaps adding resistances would be a good start in making Ice Pokemon better. I say making Ice-types resistant to Dragon attacks would be a good start, plus they could be used as a safe switch-in to Dragon-types. Maybe a resistance to Water would work, too; for a long time, I used to think Ice could resist Water, anyway, since ice is just frozen water. If Water can resist Ice, perhaps Ice can resist Water (except Scald; dealing normal damage to Ice-types with Scald would make sense).
There's probably other changes that need to be made to balance out the type system, but I don't want to spend too much time right now trying to figure them all out.
I think the poison condition got severely nerfed in Gen V. The poison-while-walking needs to come back. I also feel like basic poison is pretty weak and forgettable compared to bad poison, which is much more commonly used. The burn condition has the advantage of lowering attack. Perhaps poison should lower a stat, as well. Special Attack, perhaps? And then, Toxic could be balanced out by not lowering any stats, but would still be useful by dealing much more damage every turn. I just think basic poison needs to be equally as handy as burn.
Also, the red and blue Basculin need their own separate evolutions. I get that they're the Unova equivalent to Shellos, but Gastrodon is much more versatile than Basculin, anyway, given its extra typing. Basculin is relatively plain in comparison, and looks like it needs an evolution. Maybe the red one could evolve into a Water-Dragon sea serpent, while the blue one could evolve into a Water-Steel swordfish. (WIP names for them: Basculisk (red) and Basculade (blue)) There could even be a special way to get them: the red Basculin could evolve by being traded holding a DeepSeaTooth, while the blue Basculin could evolve by being traded holding a DeepSeaScale. (Some of those trade items do need to be less exclusive to certain Pokemon; there's beginning to be a bit too many evolutionary items in all, IMO) Speaking of evolutions, Jynx still needs her evolution. How is it that Electabuzz, Jynx, and Magmar all got their baby forms simultaneously, but Jynx got left out of an evo in Gen IV? I can already picture it:
Hi-Jynx, Ice-Psychic, obtained through trading a Jynx holding a Glacierizer, comes with the ability Cold Spell: when Hi-Jynx is hit with an Ice attack, her Special Attack increases.
I think Pokemon does need to have something new in the story. I feel like we've all grown too used to getting all 8 badges, beating the League, and fighting an evil team who wants to get their hands on a legendary Pokemon. I don't really know exactly how the story could change yet, but I think it's clear that the formula is beginning to show its age. I would actually be interested in fighting things throughout the story mode that aren't Pokemon, sort of like the encounters in PokeStar Studios; things like mechs or warriors or even using Pokemon to combat natural disasters. They wouldn't give EVs, of course, because they're not Pokemon, but things like that would make the game feel more RPG-ish.
Another thing I'd like to see is HMs being more useful both in and out of battle. I know there's the G/S Christmas hack where you can use a Fire HM to melt ice. I'd like to see a useful Fire HM in Gen VI. Maybe it could burn ice in the overworld, and deal around 70 damage in battle with a high chance of burn. Another example: maybe an Electric HM called Sparkle. Works kind of like Flash, only it's a special attack that hits more than one foe in a double battle, and doesn't have as high a chance of lowering accuracy. You could use Sparkle to light up lightbulbs to increase your field of vision in a dark warehouse, or use it to power broken-down machinery to activate drawbridges or to open doors. And perhaps Cut could be modified to have a 20% chance of lowering Defense. Strength could have a 20% chance of raising Attack. I want HMs to generally be seen as more useful than as a burden; Surf and Fly pulled it off pretty well; why not have other HMs that are just as useful?