John, I think your suggestion is correct. It makes sense. I tried to discover which elements are causing the problem so I could deal with it. However, the larger of my two projects is quite complex and includes many pre-rendered segments and some other fancy footwork. I was unable to determine where there is a duplication of FX. I tried separating the complex project into smaller and smaller segments to isolate the offending parts, but even the smallest components lead to the same strange appearance of the preview window. I may just have to live with it. The rendered product looks just fine, its just that the preview window is not good for an early review of fine details.
Thanks all for your suggestions. Any other thoughts?