The rain and sleet stopped and the sun came out, so I got some more photos of heads on buildings (other photos here and here). Some of the heads are on public buildings—schools, banks, theatres, government buildings—but a lot are on apartment buildings up near the roofline where you don’t even notice them unless you’re looking for them. Architectural exuberance!
One set of heads on a downtown building does seem to have symbolic significance. They are down low, just above the main door of this building (now a bank; I don’t know what it was originally), so you can't miss them.
I think (though we know just how much to trust me when I’m drawing conclusions about Bosnian culture) that they represent the three main ethnic groups in Bosnia: the Croats, representing the Western Europe influence, the Bosniaks, representing the Turkish influence, and the Serbs, representing the Eastern European influence. The three large centers of worship in the center of town represent this triumvirate of influence as well: the Roman Catholic cathedral, the mosque, and the Serbian Orthodox church.