I asked the largest Crusader Kings fan page on FB what bugs/imperfections most negatively impacted their game experience. This is the top ten.

[jscales]

On a related note, does AI ever try to proselytize and convert their province's culture/religion?

I can confirm they definitely do do this, it does take a little while though. Also you only have to particularly worry about converting vassals' faith. Eventually (though it may take a few generations, so arranging education of kids is faster) a character can choose to adopt your culture by themselves.