Oh, I thought the blue keylines.....(running to do more research)...Let's find out!!
OK what I did was to try and re-create what you created. I drew a box then drew a circle in the box and made the 2 a compound path. I then went to effects>3D>extrude & bevel, chose the default settings and said OK. I then went back to effects>3D>Rotate, and after agreeing to the execute this effect warning I saw the same black ghost lines like in your sample.
>> I then hit "Command + Y" to see if the "Outline" view would show any of the black lines NONE. Then when I went back to "Preview" the black lines had disappeared.
Try that and see if they don't go away!!
Maybe a little bug that Adobe needs to resolve in the redraw of the program.