Civ V was about making one thing work: proper hexagonal map mechanics. All the rest that's wrong with it will have to be fixed in future. As to unit stacking, if board wargames got this right in the 1980s I don't see why it should be done wrong now. While it was a drag to add up "stacking points" it was more realistic than one-civilian-per-tile and one-military-per-tile except of course on sea.... and forcing units to move unpredictably around when overstacked is unfit for a 'god game'. So there must be change here, though the basic idea was to get rid of the endless stacks of junk units thrown in to weaken an opponent (longswords vs. machine guns) which was impossible to convince an AI with no sense of real history not to do. I give the new map, combat and stacking rules a 6 out of 10 for this, they solve the worst problem and they point the way to the eventual long term solution for Civ VI. Which will look exactly like a 1980s high end board wargame. They got the hexagonal maps right, so they're going the right way.
Faith and religion should be distinguished by their viral, anti-national character. A national church can and should exist and it can strengthen an empire but it is also going to be very hard to impose on the conquered, and it is never going to spread beyond your colonies and thrall city-states. Degree to which a faith is identified with an empire ought to be a variable in the game, though the menu approach is fine and offers (as it should) very tough choices. Religions can be basically offensive (weakening enemy resistance by spreading your religion) or defensive (strengthening your combat in friendly cities), and ought to have some minor effects on diplomacy, perhaps improving research and trade agreements (common ethical language tends to make disputes easier to resolve, priorities easier to negotiate) but nothing major. After all the worst conflicts on Earth tend to be between co-religionists or at most sectarians, battling out who are the "real" adherents to whoever...
There should be more you can buy with Faith, not just units and buildings but perhaps advantages similar to those specific to the other civilizations like the Inca's road maintenance bonus - why shouldn't Christians be able to buy this with Faith to make a road to the Holy Land practical to maintain? Or Muslims to make the Haj? Historically that's exactly what they did. That means menu-izing some of the civ-specific bonuses, but why not? They should be expensive and difficult to obtain, maybe limited (roads to one specific holy site or all holy sites or near them?) and obviously nowhere near as much an advantage as having it from turn 1. The benefit could spread, too, so if an enhancer bought such a benefit for "their" religion, those who wanted this benefit could decide to adopt it. Again quite historically valid. Viral spreading and the actions of missionaries and inquisitors and the various buildings can be tweaked (it's hard to understand what happens to your Cathedral benefits after you inquisit the religion that built it out and install your own state religion and build a Pagoda... even harder if adherents of both religions are there). A serious problem with the Faith benefits are they are just not explained in full detail when you hover over them. This is a documentation/interface problem.
Those are unfortunately many. Explanations of workers don't mention that they are tucked into cities for safety when not needed without benefitting the production (weird and not at all valid in simulation terms, historically the rural workforce moved into cities to work in industry and excess urban workers has meant a boom in production and culture but a drop in happiness and in faith, I would say tongue in cheek). The whole "help" section is not properly linked in Wikipedia-style hypertext nor linked enough to real Wikipedia articles on the history (why not? it's not going away) for those who doubt the validity of a bonus. Strange wrongness like the way one toggles "back" vs. "purchase" in the build choice screen, or the way out toggles citizen management in the city screen, or the way it's impossible to find out why you can't buy a certain tile or can't buy one at all in the late game, when all this is easily explained by a hovering one-liner and much more normal tab-type user interface paradigms... inexcusable. Also why "more actions" on units and (worst) focus stealing when turns begin, making you move the unit the computer selected to the place you wanted the unit YOU had selected before your turn began to go.... this isn't bad design, these are *ERRORS*, these are *WRONG* ways for a user interface to behave. As was departing tabs for this odd bars-and-borders-everywhere garbage, using button borders around mode shifting tabs and so on... There's basically nothing in the City or Build screen to keep. Even just finding out what you must research to get to Navigation is annoying. You should be able to select a goal when you select your next research very easily, and let the pre-requisites be handled for you without a lot of fuss. As things are, one has to effectively memorize the entire tech tree.
Spies, well... they had more to do in Civ II and Alpha Centauri - while I like not having to waste time moving them around (just give them a % chance to be caught and be done with it, obviously spies are stowing away on existing ships and fishing fleets and diplomatic missions and need not be on a map) the interface by which they do so is clumsy and doesnt tell you what you need to know - an abstract "potential" isn't as useful as knowing the score of the civ... And why don't spies play some role in sabotaging religious trickery like missionaries, inquisitors, etc. - shouldn't they be able to defend against a few more things than other spies? Spies also could be purchasable by faith, no need to have "espionage" as a separate variable. Most spies in the real world are motivated by ideological reasons and that certainly can be called a form of faith. If spies take over where faith leaves off, why not let that be the player's strategy choice?
The mod interface has no seeming way to indicate formally which mods are known not to interact well... perhaps something like aptitude ought to be used (it's open source, guys.... knock yourselves out). That's going to get worse not better as mods proliferate. As they already have to fix Civ V pre-Gods-and-Kings bugs.