Thanks for your suggestions, I'll let you know if I have any luck!

The media objects in question are
 - isosurface {f_poly4(x,y,z,0,1,-1,0,0)}  (a double-ended curved spike)
 - torus
 - sphere

There are many isosurfaces and torii in the scene, and one central sphere.
Artifacts are most prevalent where the isosurfaces are in front of the
sphere; however there are many elsewhere and (having looked at it again)
not necessarily where objects are in front of one another.

I'm rendering in MegaPOV since a bug in POV 3.6 (relating to spline
functions being passed to macros) often causes the scene to fail to parse.

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