That reminds me: there is a bug-like issue with churches. I don't think it affects the AI*, but it can certainly affect the player.
In some scenarios, some provinces (*cough* Byzantion *cough*) start with a rather big church - but lacks one or both of the church "levels" before it. This may also occur as a result of buildings being destroyed or sold, IIRC.
The problem is not only logical, in the sense that the smaller churches are supposed to be pre-requisites for having larger ones, but also practical: you don't get as much church bonuses without the smaller churches, and the bigger church (level 3+) effectively covers the "you can build this building" graphics in the province improvement screen. It is quite possible that the player will never even know of this issue because it's so unapparent.
* I believe the AI is unaffected because it doesn't have to use the graphical interface to build things.
This problem can be event-fixed in two ways:
* The bigger, prerequisite-less church is destroyed
* The player is offered the opportunity to build the smaller, prerequisite church
Basically, one event confronting the player with the situation and offering two ways out would take care of this "bug" and even make it seem like a feature. "Our great church is in need of repairs" has such a nice ring to it...
