-I miss being able to trade food resources. Since health is gone, perhaps having certain resources could provide bonus food in conjunction with certain buildings(like grains providing bonus food with a granary)? Then we could have stuff like rice, corn, and pigs again. Historically, food was a very important consideration: Rome conquered Egypt partly because it produced a huge amount of wheat. Ottoman-occupied Serbia thrived by raising and selling pigs(the proceeds, in part, funded their aspirations for independence). The discovery of corn and potatoes in the New World changed everything for Europeans. Food resources should be way more important and varied to reflect their increased importance. If rice spawned in marshes, then you'd actually do something with a marsh other than drain it...
-Diplomacy needs more feedback, more information, and many, many more options. You should be able to cancel deals(and this should probably annoy the AI and make it suspicious of you: after all, you broke your word!). You should be able to request more specific things of the AI. A weaker AI should probably listen to you if you warn it against settling near you. And, given how strong the effect of denunciations is, they should probably be used more sparingly and AIs should look askance at any player(human or otherwise) who denounces people a lot. And they shouldn't care if their friend gets denounced by a common enemy.
-The AI's military tactics are worse than bad. Atrocious doesn't quite cover it. It clearly has severe issues with understanding even the basics of the new combat system. Which I enjoy, by the way. But it'd be vastly more enjoyable if the AI was capable of simple things like effectively besieging cities larger than a small, unwalled hamlet and protecting its vulnerable ranged-units.
-The Ottomans need a better power. Either that, or triremes and naval units in general need to be much more useful. Historically, blockades could be absolutely crippling. In CiV, they're a minor nuisance. Historically piracy was a big deal, and often state-sponsored(most famously the English and the Barbary Corsairs, who, as this power is trying to depict, were bank-rolled and encouraged in large part by the Ottomans). Piracy should be a pretty good way to raise cash, but should obviously anger your targets immensely(the Spanish were totally not cool with the English stealing all that sweet, sweet gold). Then again, I'm not sure how well the AI would handle it. Or rather, how badly.
Overall, I enjoy the game, but it clearly needs work. That's alright: it's familiar territory. I did expect better from Firaxis, but, as long they can iron out the issues and spice things up(and they certainly have a strong track-record in their favor), this'll be a pretty great game.
Some additions:
-The ability to fully heal a unit in lieu of a promotion mostly seems frustrating. It is either an entirely useless option or a complete no-brainer. I feel it takes away immensely from combat, as it essentially renders everything done to bring the unit in question down as wasted actions.
-Adding to this, the blatant inaccuracy of the combat panel is an awful design decision. Oftentimes, the result is different than what it says it will be, often vastly so. It needs to give far more information(percentage chance of outcomes X, Y, Z happening, for example) or be far more accurate(i.e. limiting combat results to match what the game tells you will happen). This decision is extremely puzzling given how important individual military units are. It becomes an even bigger issue in conjunction with the above: I have often had the combat panel tell me that I would completely destroy a unit, only for it to survive the attack, fully heal the next turn, and wipe-out my unit.