I have one idea that I'd really like represented in EU3, as it is extremely underdeveloped in every game I've seen so far and it was a major part of history.
-Internal intrigues and problems.
Almost every nation in the EU2 time period had internal problems, anything from rebellious nobles in Louis XI's France, to the English civil war, or the nobles of the sejm in Poland, or even the disintegration of hordes like the Timurid Empire or the Golden Horde. Right now they are handled by events (and not handled very well at that), and are often impersonal parts of the game that are like "wth was that all about?". Entire empires rose and fell over feuding nobles and other sectors of society.
Easily said.

If done sort of at lest how I see a good, thorough system of it, almost anywhere should be able to become independent if it's ruler is allowed too much room to breathe. Rulers should not be all powerful as they are in EU2, but should rather have to work with different factions to ensure their power. Armies should be able to mutiny if their commander is good and doesn't like or is jealous of the established institution, or they get pissed off for some reason.
Different issues and rivaling factions could and should be able to split a nation in half (a la civil war). In such a case, the player should probably have the choice of which side to take up arms with, and if they lose, still be able to continue as the other factor with their ideology and whatever things they stood for. Of course these sort of events should not be isolated but be leading up and be the result of certain choices made earlier, even if it had just been putting the wrong guy in a powerful position, or not giving those noble families that land that should rightfully be theirs.
Cities, the army and nobles should be the main factors to applease if you don't fancy the thought of a split nation. However doing that may require a little bit more power to them than you'd like, so a more likely option would be to ally one especially and use them as your power base. Get the nobles to love you and you'll have the prestigious and rich on your side, but may hurt your budget and make your focus very agrigran in nature. Get the merchants and artisans on your side and you'll probably have a good ally in business especially against nobles. Applease the army, and rule with that iron fist you've been longing for!

Just don't forget to give them a significant portion of your treasury. Anger any of them enough and expect retribution so hope you got the right allies.
Nationalism should also be a big part in internal strife, and should decrease co-operation with all factors of their society. However over time, one should at a significant cost be able to gain the respect of that area by allowing them more privileges or equal to your other areas. For the significant costs, it would take a long period of time, could annoy your original areas if you get too close, and would cost a fair amount of money in either reconciliation of two different systems, or dealing with inefficencies of two different systems. Nationialism should also include national uprisings, which could ultimately be quite nasty if co-ordinated well. (yes co-ordinated. a systematic approach to rebellions is something that is seriously lacking and until something like it is able to be incorporated, rebellions are really not going to make a whole lot of sense or be able to be shown very well).
That's sort of just touching the surface, as it could ultimately be a rather large topic and very wide encompassing. Nationialistic unrest, civil wars (whether a house, or a nation divided), inherently unstable empires (such as ak koyunlu, the steppe khanates etc), weak feudal governments (post HYW France), ambitious individuals, mutineering armies, public overthrowing of different types of government etc could all fall into this category, and are seriously needed. IRL many nations had to stop growing and look inwards instead because they simply didn't have the stable base to extend further. Internal problems were even more common than external problems were much of the time.