Let me say straight up I have only been able to play the demo so far. But what I wish to make suggestions about is in relation to the interface anyway.
The suggestions are directed at Firaxis and also modders to an extent. Especially if there is a solution (e.g. a setting in the .ini file) to any of these issues, please post it!
Please feel free to make more suggestions and if I think they're important or good ideas I'll add them to the list. I may add more as I think of or see them, especially after I get to play the game.
I also realise some of these suggestions may have been mentioned elsewhere already - sorry about that.
Critical:
Important:

Please feel free to make more suggestions and if I think they're important or good ideas I'll add them to the list. I may add more as I think of or see them, especially after I get to play the game.

I also realise some of these suggestions may have been mentioned elsewhere already - sorry about that.
Critical:
- Reduce length of camera movement after end of map-scrolling inputs.
Zoom-To-Cursor is a very nice feature and a step in the right direction for the civ UI. However there is quite a considerable time the camera keeps moving when you release the mouse's scrollwheel. A similar thing happens with regular screen-edge scrolling too. It's ok for there to be a bit of movement after one stops the input but it's about 1.5 seconds in civ5. Compared with maybe 0.4 or so seconds in civ4 where it's basically a non-issue.
Scrolling the map by click-dragging ends up winning here because it does stop moving as soon as you stop moving the mouse. Also, in strategic view the camera-lag is basically zero, making it much much faster to zoom around the map or to scroll around. - Add "No Unit Cycling" option
This option was in civ4, and for those who aren't familar with it it just means that when you give an order to a unit the focus doesn't immediately jump to another unit. It's especially critical in MP games (but I haven't played civ5 mp) but also for easier micromanaging of units in single player. Suppose I want to put 1 worker turn into building a road but next turn I want to start building a quarry (because I get the tech for it in one turn). What I would like to be able to do is give the order, then immediatley press the cancel button. As it is now, giving the order causes the screen to jump to who knows where, selecting another unit and I need to scroll back to that worker to tell him to stop.
I consider this game option to be absolutely critical to the interface and I never play civ4 without it. I don't think it would be difficult to implement either.
Important:
- City screen: Disable map scrolling and allow user to exit screen by clicking map
Not entirely sure why, but you can scroll around the map while inside the city screen. I could understand maybe allowing the user to zoom in or out centered on the selected city, but not scrolling to the other side of the world. Allowing the user to click the map to exit the city screen would make a convenient shortcut for people relying mainly on the mouse, without having to press enter or escape or nagivate to the tiny return-to-map button at the bottom of the screen. - Input boxes should have default focus.
For example, when saving the game or renaming a city, the user shouldn't have to use the mouse to click the box before being able to enter something into it. Especially since the user can't do anything else until the input box is gone, it makes no sense for the input box not to have the focus straight away. - Draggable mini-map
In civ4 you could scroll the map by clicking and holding on locations in the mini-map. In civ4 this was one of the fastest ways to scroll around. It seems in civ5 this has been forgotten (unless there are technical reasons for avoiding it), and click and holding the minimap does not move the camera position until you release the mouse button. - Allow/fix alt-tabbing
I feared this would happen with civ5 being a steamworks game, but I haven't found a way to alt-tab out of the (fullscreen) game. This is a major drag, but there may be technical reasons for this problem I'm not aware of. - Show unit hitpoints as a number - not only a bar
While an injured unit does have a tiny little health bar showing its health, it is quite difficult with normal healthy eyes to be able to tell exactly how many hitpoints it has out of 10. I don't mind where on the interface this info is displayed, but it needs to at least be shown somewhere. - When giving "Heal" order, show number of turns.
Pretty self-explanatory really. This should be a really simple change to make as well. The need for this would be slightly reduced if the hitpoints were shown as a number, but even with that fixed it'd still be nice to see how many turns anyway, so you don't even need to think about dividing (10 - hitpoints) by 2 if in friendly territory or 1 if in neutral territory. - Disable most keyboard shortcuts while civilopedia is open.
At the moment it's too easy to accidentally give an order to a unit (which you can't even see because the pedia is taking up the screen). e.g. if you accidentally miss clicking the search box and start typing something before you realise, who knows what commands you might accidentally issue to units?
- Provide detailed unit mouseovers
At the moment when you mouse over a unit all you are told is what the name of the unit is. Often there are times when it would be nice to not have to deselect the active unit just to check the promotions or somesuch on another unit. - When choosing production in a city, exiting city screen should close the production-choice window as well.
Some may disagree on this. In general it seems there is quite a lot of work that can be done on the production-choosing window anyway, including keyboard shortcuts for easier queueing and so on. - Shift clicking to set waypoints for units.
Just like in civ4. If you're trying to send a unit quite some distance and there's a hostile city in between, setting a waypoint that ensures the city is safely avoided would save a lot of time from having to babysit the unit on its course. At the moment, the path-finding can take your unit right past the bombard range of an enemy city. - Remember last active strategic overlay on saving game.
Not a big issue, but it's nice if when you load a gamesave most of your interface settings are remembered. This includes the chosen overlay mode for strategic view, IMO. I think it already remembers your choices on hexgrid, tileyields, resource flags etc., but I may be mistaken.