can't say for sure (I'm barely far enough along), but it could be the texturing; maybe it's an artifact of tiling. You could increase the size of the jpg, bmp, etc.

only other thing (not as likely) I can think of is maybe the model has triangles as faces. Poser doesn't like triangular faces. Mebbe if you can convert them to quadrangles (4-sided face), which might make them go away.

more helpful answers to follow this..;)

This takes more work, but it seems to be more compatible with Poser
than the all-angles result of a Boolean.

Here's a quick and ugly sample, which at least shows the principle.  

I can see why poser is interpreting those triangles wrong. the way the booleans worked out, it almost looks as if some polygons are connected to others in a geometrically contradictory manner, like a moebius strip.

This is a very common problem when using booleans for modeling, or when exporting from a modeling software to Poser. Ockham's sugestion is one of the easiest ways to control the ceation of narrow triangles. Depending on the software you are using, there may be some other options to fiX the model without recreating your arches/windows (but it may be just as much work). 

One option that may work if your modeling software has the ability to "cut" the mesh, you can create a square/rectangular frame enclosing the problem areas, then force (weld) the triangle verticies at the new corners. You will still have a lot of triangles, but they will be shorter and usually less of a problem in Poser.

Another option would be to manually re-cut the model with lines extending perpendicular to the edges from the arch/window to the edge, then either manually merge the triangles into quads, or if  your software supports it, you can do an auto convert from triangle to quads.

Unfortunately, I don't know of an easy way to "fix" the model. If you could let us know what software you used to create the model, maybe one of the gurus could give you a simple fix. There could be an option within the software to force the creation of quads, which would be the easiest fix.

Anim8or
UVMapperPro
Poser7

You are in trouble!
The only way to avoid this problem is to create some vertice in the planar face and let the triangles join to this point..