There's two things I'd like to see though introduced:
"Pairing Pokemon". I've had this idea based on the "Bonds" mentioned in the trailer, basically you could pair up two Pokemon in your party. They'd provide each other with a small stat boost, based on their base stats (like covering for the other's statistical weaknesses a bit?), and their could also be species-based "Support Abilities" that aid their partner when they're in battle. This would be mainly for Single Battles, though, not Double Battles where Pokemon already cover each other. As their Bonds grow, the stat boosts would grow too, and the Support Abilities would have better chance of activation.
I was thinking this could open a lot of new Evolution possibilities, as Pokemon could evolve when Max Bonding with another. Sylveon I feel could represent this...it evolves from Eevee when Max Bonding with any Pokemon. Then I thought of some more detailed ones, like a Fire Pokemon and an Ice Pokemon evolving together when they Max Bond into two separate Pokemon of the same species representing a balance between Fire and Ice, non-equilibrium thermodynamics. Or a "Miko" Pokemon that evolves into an Onmyouji Pokemon when Max Bonding with a Ghost Pokemon as it learns to tame spirits...and if its Banette, it also evolves into a Jiangshi-inspired Pokemon, as it's now a servant to the Onmouji and its grudge erased.
The second one is it'd be cool to see three-way battles, like one between the Starter Pokemon at the beginning of the game. You'd have to change around some mechanics to make it fair, like perhaps weakening damage if the same Pokemon's attacked by both sides, but it'd be neat for a few event battles.