I'll be the boring one: better GUI. It wasn't particularly bad, but it's something that could always be improved.
I find this quite a good point in fact. the minimalistic interface in EU:Rome 1 was a good indication of how underexploited the game was.
taking Rome1 as a reference I can speak of things that could be improved like:
* the religious minigame (I hated that thing, click randomly to get a random result) make it proper or get rid of it.
* the "ministers"/tecnologies minigame, things were happening so slowly that you hardly had a feeling that it mattered at all. Also there was nothing to do with them other than fulfilling people's ambitions.
* the characters, messy, very messy, you had a lot of options to do with people but as you had no communication with the game you could hardly understand where a risk was happening or a guy was getting powerful or angry. the options and characters were ok but more "stuff" happening (and making the player notice it) would help to get yourself being more involved, I mean, to play.
* the war game, I found a bit dull to be able to have 50K guys in some province for years like nothing. it should be far more complicated. History tells that big lost/won battles were able to crumble empires. if your army is destroyed you have no easy way to recover.
* the resources/trade minigame. by the capitoline triad please please! get rid of that ... thing. in general please do not create artificial rules/processes that do not look real. 1 resource only able to be trade to 1 province?
*the senate, great concept but I think underexploited. IMHO it needs mostly a CK approach in order to make you able to play more with it and factions actually being composed of people with clients, networks of contracts/favors/relations that you can use and manipulate.
* colonization i do understand it has to be slow but probably it could work better if mixed with some area of influence or trade power or... something in that line in order to make the player playing more and being able to actually do something about it and make choices. this adn the other aspects of the game had
basically the same problem, a worrying lack of decissions to be made. in general the game was too much of waiting for something to be available then enable it because there is basically no reason why not.
I am not trying to be mean, just some things that I find could be lessons to be learned. I know, this is the easy part, the really tough thing is to give ideas but hey! I never said I am good at anything but complaining
nah, a small idea/story on how I would llike to see the game performing.
Say I want to build a temple in Siracusa*** it may happen because:
1) some local character wants to do it to get prestige, manage the contractors and get political power or gives him control on something in the city or the province (trade, mines, religion,...)
2) the ruler wants to do it, if there is a senate then it must be voted and then the game of interests starts for the same reasons as above but dealing with factions.
Ideally I woud see all this working "like" in CK with counts/dukes/kings but with no feudal organization, of course. a game of influence and resources control rather than feuds.
*** This just reminded me of something that I think is nice to differentiate, no more province-only maps. If there is something remarkable of ancient world is the urban society, if you leave this out the game is "just another province-based wargame". The map should be a mix of provinces and big cities (in my dreams they can appear and disappear, no hardcoded capitals, if you are a paradox dev or PM you are allowed to hate me for this

). the things that you can do, the interface, in provinces should be different than the cities. a focus on resouces and manpower for the provinces, for instance, and politics/culture/trade/army-supplies for the cities, just a quick example on how the different types may be designed.
tl;dr