Disclaimer: I only ever actually played a little of CiV after spending an enormous time on I, II, III and IV.
First off, the thing I definitely like most about the one unit per tile system with ranged units and combined with the trade system is that naval units matter now! Playing through the game I actually felt that my navy was as, if not more, important as my land based armies. I NEVER felt that way once in any of my earlier Civ games (except in a couple of the few V games I played). It really made the experience feel like an improvement.
Which leads to my primary comment for adjustment about the yet-to be patched version (which all strategy games must undergo after release. I honestly don't know why everyone always makes a big fuss about it really). The AI just doesn't prioritize the right stuff. I actually don't think trade is outlandishly imbalanced like so many have implied. It does benefit both sides afterall. It needs to be toned down a bit (which Firaxis did announce already) but completely nerfing it would ruin so much potential.
The AI should build large navies, aggressively go after trade in wars, group its ships, avoid outnumbered confrontations in favor of pillaging, and engage in naval battles when it has the numerical and/or technological superiority. I only encountered a couple warships in all my wars in my first game. Had the AI gone after my trade and made it difficult for me to sail fleets up to their cities and shell them, then I would've had at least a real fight on my hands.
Diplomacy and options available should also be ramped up. AI's (depending on relationships and personality) should use trade blockades, embargoes, etc. aggressively against warmongers or anyone nearing a victory condition. War should be more of a trade off. Steamrolling opponents with no consequences to balance isn't fun.
Speaking of war: where's the spectrum of benefits? Health penalties/bonus are being amped (rightfully so) but when I went to war, I felt there was no point in not completely steamrolling my opponent. This was both tedious and, well, without much reward.
Healthwise I don't need a bunch of puppet or, worse, additional cities and razing takes too long and confers practically no benefit. Since a large number of cities is not beneficial and as it takes so long to grow a city into something resembling maturity settling the now open land is not a viable option either.
However, there are no reasonable diplomatic options that make non-complete victory worth it. I should be able to force my opponent to suspend trade with another for a set number of turns or to reserve a certain % of their routes for my cities exclusively. There should be affinity related options subject to the affinities and levels of both parties. Quests should be activated for both sides during the war.
Obviously, you can already take resources but that's not properly developed. What does a Supremacy Civ gain from defeating a Purity Civ and taking Floatstone? Either there should be some use for all the resources for every Affinity (while maintaining greater use and value for the affinity-associated resource) or, and I'm spitballing here, you should be able to trade the ability to build special units/buildings.
Example: for 10 turns Supremacy Civ A can build a unique floatstone Supremacy unit due to a treaty with Purity Civ B. As soon as the agreement ends, Civ B stops supplying the necessary equipment to build the unit so Civ A can only maintain the ones it already built. If Civ A does not maintain its Floatstone supply then the units are inactive until enough is acquired. Perhaps the agreement costs Civ B some production for X number of it's largest cities. Therefore Civ A has incentives both to not completely annihilate Civ B and also to more or less maintain the status quo post victory. Civ B may chafe under the yoke, but it survives, has some leverage in the agreement and as Civ A becomes more reliant on the relationship, can make a comeback. More fun than just steamrolling.