It always annoyed me that muslims have churches in their provinces; they should have their own mosque structure. Assuming that muslims will be playable in CKII, there should be a separate tech tree to cover each religious group.
Furthermore, when a christian takes a muslim province they should have an event whereby they can convert a mosque to a church (or vice versa if playing a muslim dynasty). Im thinking if you force a conversion it will reduce peasant and clergy/imman loyalty, or you could rely on you diocese bishop to try and convert the masses peacefully.
Also, many people have asked for an enhanced trade system, similar to EUIII. I suggest that a ruler should be able to fund trading companies, who then do their own thing, but give a slice of profits to their liege. You should be able to build permanent trading posts between two provinces (think along the lines of EU:Rome), so setting one up with, say Venice, could be very profitable. The trade link could also serve as an additional way of spreading techs/disease between non-neighbouring provinces. As you tech tree advances, you would be able to have additional trade links.
Yeah, we should have some sort of mosque buildings for musilms in the game, along with more fleshed out events and countries.