My list:
City state defense/unit gifting quests need to remain viable even if they return to peace with the enemy.
City state bullying quests are really only achievable if the placement of the city state is convenient. Most the time on Immortal and Diety level I think how inopportune it would be to move a large enough army to actually demand tribute (and the window of time is too small as well)
The fact that you cannot pay to put a citizen on a tile/make workable a tile in your territory that is beyond the 3rd ring of your city. I'm a completionist and I want that damn fish out there in my border to be workable by my city.
The fact that sometimes you can't lock a citizen on a tile and must switch to the appropriate focus (food, production) to try and get the desired affect with that citizen. This is especially annoying surrounding lead up turns to starting a wonder or constructing a wonder itself.
Desert and tundra spawning too close together, especially near starting locations. This provides a "Sophie's Choice" when founding a pantheon that often leads to me re-rolling instead.
Barbarians spawning with advantage (often from an out of sight camp) and moving to capture a worker or attack a unit instantly. Camps themselves are an acceptable random event, but the priority move is akin to a disaster event in unpredictability and causing a change of plans.
The fact that there are no promotions to choose from when a spy levels up and that their sight radius remains the same.
The fact the the God of War pantheon belief is arguably a "God of Defense" in it's execution. To use it in war you must forward settle AND plan to get your pantheon or religion in that city asap (somehow?)
Leads me to my next nitpick - pantheon followers. Religion is just a big mess until religions are actually established. I still haven't figured out what's going on with the spread of pantheons. Sometimes you have the belief in all of your cities and sometimes you need to use a missionary. I also find it the opposite of fun, and thus a bad mechanic, that pantheon beliefs can be lost if someone's religion overpowers your pantheon before you can found a religion. They should persist as cultural flavor, much as superstitions do in the real world.
The displayed number for construction is not always mathematically pinpoint accurate (taking into account that factors such as happiness and golden ages have not changed during construction). I don't know how to reproduce or explain this one but it has infuriated me on occasion with the failure to construct a wonder. Perhaps it's only my imagination.
That you can't always build 2 of the same unit back to back in the same number of turns (i.e. workboat A takes 1 turn, workboat B requires 2 turns). I often switch to something else and just go back to building it in 1 turn much later citing "WTH?" as my reason. People constructing work boats should become more specialized if anything, not take literally twice as long the second time around.
That policy saving doesn't let you save free policies.
That no civ has a UA bonus based on the liberation mechanic (USA for example). This would be interesting because you can never know for sure the intentions, whether it was done for ethical reasons, diplomatic reasons, or purely for selfish reasons.
That no civ is naturally good at catching up at tech (Japan for example). The World Congress will offer a catch-up mechanic but I still like this idea for a civ like Japan. It could work like Ancient Regime did by tapering off late game and offering great historical flavor.
That no civ naturally favors the early annexation of cities. (Denmark would be great for this.) I suggest they retain a much greater portion of buildings upon capture. Perhaps in some way religion could work as a taper against this behavior as Christianity brought about a change about in the real Vikings.
That there is no mode of play that encourages remaining in each era for ongoing time-period tactics employing all the units (horsemen, composite bows, spearmen, galleys). Instead it is an arms race that often ignores parts of the tech tree, defying warfare conventions. (Yes I still intend this in lieu of there being a marathon speed).
Lastly, I think that as far as attacks being able to pillage tiles, I vote that that only be done by A-bombs, nukes, and GUIDED MISSILES. Give those crumby little missiles a purpose. They don't do splash damage so increase their viability.