Try again using open paths. Remove the vertical segments at the right of the two paths.
Note that Illustrator's 3-D effects are crap and have been in beta since they were introduced.
No changes with an open path. Thanks for the suggestion. What did help partially, was applying the effect to a filled shape, instead of a stroked one, as I was doing first. That made the artifacts in the top part disappear.
Did not know 3D effects were still in beta. That is not something they tell you when buying the package, as far as I was aware. Note that I am still using CS3; the problem might be gone in CS4?
Edit: just changed the metal pin from stroke to fill also, this appears to solve the problem.
Adobe won't say that Illustrator's features are in beta, but just using them, or really Illustrator in general, will tell you differently.
Well, at least I found this in the help files:
Note: 3D objects may display anti-aliasing artifacts on screen, but these artifacts won’t print or appear in artwork optimized for the web.
—Creating 3D Objects
Anyway, I do not think it is directly related to my problem though; sounds more like this:Strange wirefram fragments in 3d revolve