Keep the hex and 1UPT (back bone of the new combat system. You never have to contend with the RNG ever again! Plus, proper ranged Combat).
Keep the leader Animations and interface.
The importance of Gold could probably scaled back a bit.
Adopt something similar to the Civ IV approach - you can only buy things with gold once you reach the appropriate technology (Civ IV did it with civics, but in Civ V you can't make an ability that critical a Social Policy). Even if this is only Currency it means no early settler/worker gold spam or gold rush armies. In terms of the tech tree it also represents a choice between early rushing to RAs or early rushing to Currency on a different strand of the tech tree.
Although, some Civ 4 elements would be nice. Such as The Victory Conditions (these seem more thought out than the ones here. Domination while being peaceful the whole time? Sign me up!)
Thought out in a different way - I'm not sure it's a sign of being better thought-out that two of the victory conditions were essentially identical except for the proportion of the population/land you needed to control (diplo was autowin if over 50%, domination if over - IIRC - 70).
Then again with the reshuffled tech tree it's not very well thought-out that you need higher tech to get diplomatic victory in Civ V than to get space victory, and that the tech paths leading to each don't diverge that much until very late in the game. All victories except Domination are more heavily tech-dependent than in previous Civs. Domination is fine; "peaceful domination" is called diplomacy, and it should be the case that the two victory conditions have separate play requirements to achieve.
and city maintenance (that is, no Building and Unit Maintenance and free roads).
This was one of the weakest elements of Civ IV, and I like the addition of road maintenance costs. It's possible it might work slightly better with Civ V's slower production rates, but there's nothing interesting strategically about a game where you can build infinite duplicates of every building you want without penalty, and in which production times are so fast that you can even do it without meaningful trade-offs between producing units and producing buildings.
It was also simply a flawed design concept, as were its predecessors - city maintenance and corruption existed for one reason only: to try and ban a particular strategy (ICS). Civ V certainly hasn't hit the nail on the head in its attempt to rebalance tall vs. wide, but it's a better approach to try and make alternative approaches competitive rather than design a system in which one way of playing is so inherently superior to all others that it has to be actively restricted or prevented in order to allow for more varied playstyles. So far Civ V has developed a system that works at the extremes - "true" ICS with one city literally everywhere you can place one is doable but is a weaker strategy than most alternatives - but not for most forms of play: until you reach those extremes, wide beats tall in most cases (selection of tall-focused civs notwithstanding).
I also liked how in Civ 4, you need to research Currency (?) before you can trade Gold. Being able to trade Gold since the dawn of man to when Mechs walk the earth implies that there is only one global currency and that's too close to Revelations for comfort (although, there is a real-world impetus for this. As economies collapse, the only hedge you have for the new world would be precious metals).
The earliest Civ games (maybe just Civ, but I think also Civ II) had Trade as an early technology, and nothing was tradeable until you'd reached it (Civ I also had trade caravans as the only mechanism for trade, and these were unlocked only with this technology). That would be nice to have back (the Trade technology, not the caravans). So Trade would unlock trade in luxury resources (barter, effectively), and Currency trade in gold - I think that would be a good system.
Combine some others, for example: keep all happiness local to your cities until trade routes between your cities get established, but now connected resources will only provide a certain percentage to other cities. Probably provide the happiness only when the resource is worked. Also, keep the UA/UB thing but also provide leader traits.
Mechanically, happiness local to cities doesn't perform the same function as global happiness. Adding some kind of local-scale population management seems likely in a later incarnation of the game, but it shouldn't be at the expense of the global happiness system and would serve a different purpose - likely production lost (population refuses to work tiles) if the city is "unhappy" rather than the global growth penalty. It would be similar to the Civ IV dual management system (happiness and health), but without the redundancy introduced by both being local scale and being managed in essentially the same way.
And refine completely: Diplomacy.
For the first time in the series, Civ diplomacy now has a strong baseline from which to work - the system is a very good basis for the additions of further options (not to mention AI improvements) rather than just a trade window to which extra types of modifiers can be added. This is I think the case with much that's in Civ V - it all feels like a very promising base for subsequent games (while Civ IV represented more the pinnacle of what can be wrung out of what was by then an increasingly dated game engine).
1UPT and the game design changes to support this (generally low production, global happiness etc.) really soured me on Civ5
I'm not sure where the common belief that these are intrinsically linked springs from. There's no requirement at all for 1UPT to slow production for anything other than units. I don't see any link at all to global happiness, which is a maintenance system to limit population. Rather Civ V's engine is designed around trade-offs - production is slower in order to force the player to make choices about what to build when rather than just spamming anything and everything because there's little or no cost to doing so. Global happiness is a constraint on ICS-type strategies that works by giving you a fixed amount of "population points" (happiness) that you essentially distribute around the landscape, either as many in a few cities, a few in many cities, or various permutations inbetween. It's like a slider for city size vs. number.
* More emergent civ characteristics and abilities, based on past actions, terrain, perhaps even 'picks' at the start as many space 4x games have
Space 4x games have the advantage that they aren't working with factions intended to represent historical civs. Civilization isn't a game about "building an empire" - any number of games do that. It's a game about "building the Roman/Mayan/Incan/Siamese/etc. empire". It's a large part of the point and the feel that civs have their set, defined characteristics. Something like a 'reputation' system that, based on past actions, affects how other civs see you (now common in most empire games, although in most cases this is a fixed racial trait rather than something that changes over time) would be a nice addition, though.
* A fun system of revolutions, social factionalism, empire splits etc. - basically not to just limit the player's enemies to other nation states, which seems somewhat reductive
I miss the civil wars from past games, but it's a key element of Civ - and indeed of most 4x games -that your rivals are indeed comparable empires to your own; other elements turn up as random events, but the barbarians, pirates, rebels etc. are not major enemies, and in most gameplay senses behave just like other civs anyway. I wonder if they could add something like Sins of a Solar Empire's or Distant Worlds' bribery system, where you can "bid" with other civs to pay off the barbarians so they'll attack your rival instead.
* Representation of significant developments in more modern human history hitherto often ignored or trivilised in civ (certainly in civV) with new systems in place to explore them e.g. not +20% gold style representations. Including the following: industrialisation, capitalism, terrorism, environmental damage, multinational corporations, class war
Class war is hardly something relevant in a Civ-type game; capitalism is covered under policy/civic selections and consequent effects on diplomacy (although selecting Commerce doesn't have any diplomatic ramifications). Most of the others have been treated in past Civs; Civ V handles religion better than Civ IV did, it may be able to revive corporations and make them work (could be a late-game way of using some of those strategic resources you won't otherwise get much use from, or of generating new resources the way mercantile CSes do). I don't know why environmental damage was removed from Civ V - I'd be fine with re-adding a pollution/global warming mechanic.
* Diplomacy presented as something more than barter. A system for concepts like bluffing, threatening, sucking up. Depth and a roleplaying element to be present.
Civ V represents an advance in that regard, but I agree more can be done. You can certainly be threatened (I remember a game where Attila parked rams nearby then popped up to ask if I minded him bullying a city-state under my protection). And it's hard not to see the guy who denounces you for half the game but is never in a position to do anything about it as doing anything other than bluffing. But a lot of these are concepts that exist in the interpretation - it's not something you can really program in mechanically. Where I see Attila engaging in gunboat diplomacy, someone else might just see a "Sorry I bullied your CS - choose Option A or Option B" screen.
* Change in scale of 'pieces' over time to avoid later game tedium of dealing with hundreds of cities/units. Start by moving around individual units and building with cities, while by the end of the game I want each vast territory or army to be represented as one 'piece' in the game.
I think a 'control group' system would resolve this, and as such it's just an interface issue. Let me select more than one unit at a time (with shift-click or ctrl-click), set a destination, and the whole group will move there. Stick arrows on the city bars and the city interface screen so that you can scroll immediately to the next rather than having to locate it on the map or in the Cities screen.