I'm not really an expert in game design and balance, but here are my two cents. Please feel free to criticize and contribute:
For simplicity's sake:
- A new Ruler Demesne map mode (which showed not only your ruler's, but also everyone else's (If I recall correctly, other rulers' titles can already be seen in their characters pages, but to find where their counties are located you need to click on each one of them, one at a time, which is somewhat cumbersome).
- The return of the game summary feature from EUIII that chronicled the history of your dynasty (and if possible, make it less repetitive and more like an actual history book).
- Give the "arrange marriage" UI a new tab/sorting option to more easily find out characters that would accept matrilineal marriages.
- The ability to search for characters by name, just like you can search titles
And for fun's sake:
- Some more permanent solution added to the intrigue mechanics when it comes to your dukes scheming against you. A sort of compromise between asking to end a plot and imprisonment, something that don't force me to choose between risking (yet another) rebellion, and asking my scheming duke to pretty please not steal the Kingdom of Ireland from me because I know EVERYTHING about his plan and his backers just for him to two weeks later start the same scheme again. Often with the same backers.
- The ability to rename your Kingdom (possibly at the cost of prestige, if there must for some reason be a cost involved) and, more ahistorically, for a ruler with sufficiently high prestige to create an entirely new Imperial/Kingdom title out of nowhere (I'm thinking a ruler being able to declare the Empire of Iberia, or somesuch) that wouldn't GIVE prestige when created, but COST a high (I'm thinking in the house of the thousand or two thousands) amount of prestige since it's basically your ruler being megalomaniac, and that would start VERY weak (relation penalties with both your dukes, your immediate neighbors and possibly The Pope, as well as increased revolt risk) but that would gradually stabilize itself and come to be accepted both internally and externally (perhaps by being sanctioned by the Pope).