I've been in the beta, but I never really played it during that time. So my game yesterday was my first real session.
I'm going to list a few things I had difficulties with (from a game design point). Disclaimer: I played a lot of Civ 4: Colonization the last few days. So I might be influenced by it's interface.
Active Unit
There is no easy way to see in a split second if the current selected unit has moves left or not. Sure I can check the top left list to see units with moves left or look at the number of moves the unit has remaining, but that feels slow for me.
Suggestion: The selection square when clicking on a unit it could i.e. blink or glow or something if the unit has moves left. OR if the unit has no more moves left deselect it.
Special Ressources
On my first game it took me an hour or so to figure out I actually have to build something on the fertile land to gain its ressources. The problem for me was that I don't build it from the city production selection window but rather by clicking on the ressource itself. Is the fertile ground building built seperately from the normal city building queue?
City Building
Cities without a queued building are yellow in the top left overview. BUT they are yellow even if no build options for the city are available. So bascially I have to check those cities every few turns for newly availabel buildings.
Unit Movement
In Civ 4: Col I can preview the route the unit might take by pressing and holding the right mouse button. It would also help to see its current path if you select a unit with a move order. I could use some kind of feedback if a unit can't pass over a mountain or a coast line 
Equipment handling
I have a stack of "hero" units and my sovereign. I select the "inventory" button of my sovereign to change out some equipment. It would be nice if I can switch to the other units of that stack without having to close the inventory first.
That's what I can think of for the moment.
If you guys have some tips how I can handle some of those points better let me know. 