I think folks have used the general term "shadowed", as in "odd, unexpected shadowing".  *Trimangulated* is more evocative;  I like that. :D

     Yes, many older models, especially those made for P4/PP (Poser 4 Pro Pack) have this sort of problem.  With P4 models, it's usually a mesh with some normals pointing out, and some pointing in.  P4 paid no attention to it, but with the release of P5, they showed up.

     If the entire polygon is evenly shadowed, look for a flipped normal, or a duplicate polygon sharing the same space.

     If the poly has shadow stronger toward one vertex or edge, then look for an extra vertex in the poly which is out of plane with the others, or perhaps what looks like a straight edge is actually interrupted by a vertex, making it two sidea of the poly.  Poser will render a strictly convex n-gon without problem, but if any angle is concave or even precisely 180' (i.e., two edges in a straight line), you'll see artefact.

     Merge is a modeler command;  If you have duplicated vertices, it will merge any two (or more) vertices which are sharing space.

     The blue poly looks like a quad but actually has six vertices, and the two vertical sides each have two end-to-end edges in a straight line.  Thus it is a hexagon which is not strictly convex.  It is an ebil, tricksie polygon, and Poser hates it forever.

     The ruddy polygon on top looks like a triangle, but has a fourth vertex, displaced upward out of the plane.  This is a quad which is %@$#'ed up like a soup sandwich.  Guaranteed render artefact.  Also, notice at the corner of the box, there are two vertices, and they are not connected (I've pulled one up a bit to make their separation apparent).

Poser 12, in feet.  

OSes:  Win7Prox64, Win7Ultx64

Silo Pro 2.5.6 64bit, Vue Infinite 2014.7, Genetica 4.0 Studio, UV Mapper Pro, UV Layout Pro, PhotoImpact X3, GIF Animator 5