What exactly is the structural issue. Does it prevent any light fixture from being used on the ceiling?

A chandelier by itself will likely cast more shadows than a light above the mirror so I think you will be relatively well off with just that fixture. That said with more lighting sources you will reduce the shadows even more.

My main concern would be, how well can a person see themselves in the mirror, relative to lighting at the wall above or beside the mirror? Say a guy is trying to shave his neck, is his head throwing a shadow onto it?

Karin L

The answer really depends on where the light source is relative to the object you want lighted. A good surface mount light behind the individual will provide adequate but noit great lighting because some light will be reflected from the mirror onto the face. The optimal solution would be a combination of sconces or over mirror lights in combination light placed behind.