I'm guessing some of these have been covered, but this is what gets my teeth gnashing.
1. Improve the tile selection algorithm so that (in the case of puppeted cities at least) gold focus is not completely at the expense of growth. A 1 pop puppeted city working a desert incense tile does my head in when there's a food with slightly less gold tile available.
2. Improve the autoscout algorithm so that it avoids city state territory and barbarians. I never automate scouts now and and it really annoys me that I have to manually explore maps.
3. Allow the user to set an auto response to AI civ messages. If I've got every city state under my protection, I don't want to have to tell numerous civs turn after turn "you will pay" for extorting that city state. This is one of my biggest irritations by far. On immortal difficulty I feel like I'm doing this every other turn.
4. Add the ability to tie workers to a particular city for autoworking purposes. Add the ability to queue tasks.
5. Make border growth manually selectable by the user, as the Governor is an idiot, especially in early game when getting the correct resources can make or break. Queuing for this would also be good.
6. Work boats and sea tiles..... NGGGHGG! Considering that work boats are one-use only, coupled with the fact that they aren't considerably cheaper than workers, the end result of improving sea resources is utterly underwhelming. I wouldn't mind using work boats if the outlay was worth the return, but it isn't. This system for improving sea tiles is rubbish. I generally re-roll starts with heavy sea luxuries, as it kills me having to buy/build the work boats. I know work boats have been this way for a while, but it really needs a rethink. The other irritation is not being able to improve sea resources if the city isnt on the coast and doesn't have a coastal city nearby that can send a work boat over. It's bonkers.
6. Stop using the size of the AI army to determine whether staying at war is worthwhile. 0 kills to 20 deaths over the space of 10 turns should be enough for the AI to realise that this war is a waste of time, regardless of how many other units they have ready to join the meat grinder.
7. Stop the AI building wonders it has no need for. Ghandi beating me to Petra when he only has one flood plain title adjacent to his capital is a real kick in the nuts.
8. Healing units through experience is too strong at the moment. If a unit heals instead of taking a promotion, it should not be able to attack the following turn. The current system is cheap. I hate it. And I hate doing it.
9. How about when you open the trade window up to sell a luxury, it just defaults to the standard price for what you are selling (240gp per lux, or 45gp per strat). How about the AI stops throwing in requests to add all your iron or horses to the deal, especially when it's happy to do the deal without them. This is just annoying.
10. Didn't there use to be an option to "keep this map" when you started a new game? Maybe I'm dreaming, but the option to re-roll the map without returninig to the main menu would be nice.
11. Definitely make all the diplomacy screens accassible when you are talking to the AI. Blindly declaring friendship with someone you didn't realise was universally despised isn't fun.
There's probably more I can't think of.