Most of the posts seem to be more in line with how to fix Civ V rather that what would be cool to explore in a new game, which is fine, but I would like to see a more dynamic game where players are not limited to pre defined civilizations. I'd prefer to design my own civilization and have the opportunity to make decisions over the coarse of the game which would have dramatic effect on how my civ develops. I would like to have the opportunity to choose what my unique components are and be able to choose their appearance (from a list of choices) on reaching milestones throughout the game.
I would also like to see NPC civs change through time. Leaders and strategies should change as the world changes. Civ rise and fall, split, combine and fracture. Civil wars and revolutions are fought. Government types change (original civ had government types changeable).
Random events as well as consequents based events would be interesting. Spread to far to fast, loose a war or city, work your citizens to the bone, overtax, etc as well as famine, disease, pollution (another original civ component) natural disasters etc.
CivBE introduces a satellite layer which presents a lot of creative possibilities. Eventually space stations and spy sats, orbital weapon platforms and even orbital cities. A similar layer for the oceans would be neat. Undersea mining, submersed and floating cities, traulers, and oceanic energy development.
With the interesting approach to the tech tree in BE there is the possibility to change the way tech works so that if you are first to build the tech you get a bonus to developing the sub techs or only have the choice to develop one of the sub techs. Unique units could be tied to these choices.
It would be nice to see the game go way into the future. Don't like the game ending where it does with the future tech so release DLC that adds eras to the game. If modders can do this why not the developers.
Make NPC civ more ambiguous. Are the Roman you encounter from a roman city state or from a full blown roman civilization. Spawn new civ constantly as the game progresses, perhaps using historical spawning dates as an option. Units should look unique for any given civ like many of the mods available.
Black ops could be used to affect the game anonymously. Pay pirates to raid shipping. Assassinate leaders to throw the government into disarray or kill of great people. Sabotage city buildings. Inside revolt. Use propaganda. Establish binding treaties with real consequences for betrayal.
DLC should be more diverse. Alien invasion, global warming, impending astroid impact can you work together to avoid extinction. Resource depletion, over farming, erosion.
I've never done a mod, but from what I've seen there aren't really any impossibilities listed above given the state of the game as of CivBE. Everything above should be possible. The trick is to have everything balance.
I put this together quickly and have not put any time into details I've just rambled on what has come to mind over the last few minutes, so please treat me kindly.