Richardson, I scaled up with a cube and got the same results (not shown). I did use the default infinite lights which Poser doesn't allow to parent to the cube.

I rendered the scaled up (1000%) pz3 in P5 and got similar refraction disc artifacts, but spotted (a clue?). However the transparent ball intersection with the checkered ball had no artifacts, scaled up in P5 (not shown here).

odf, Curious about the bump map thing, I applied a Turbulence node to the bump node of the checkered ball in P6, unscaled. The refracted bump looked OK but the intersection artifacts were still there (not shown). I added James HiRes with bump map in front of the checkered ball and behind the lens (see the turbulence bump on the ball). I disconnected the bump map for the Head (so I could examine the eyes).

The refraction bump map artifacts are there, just like odf's renders, for the body. Are bitmap bump maps a culprit but not procedural bump maps? Also look at the eyes. The right eye is all of a sudden looking way left and penetrates the lower lid. Is that the pupil still looking straight? The left eye looks straighter, but also penetrates the lower lid,and there's some horizontal artifact cutting across the lower left iris.

This gets curiouser and curiouser.