On Wikipedia under Preferences/Appearance I switched on the Modern Skin. Going to any article, I see "edit this page" and "edit source" links at the top. But clicking on "edit this page" has no effect; the visual editor is not switched on.
This bug consists of two different parts:
Part 1 is the fact, that Modern skin isn't compatible with VE (probably the missing #content).
Part 2 is the fact, that even though Modern skin isn't compatible with VE, the editing tab for VE is still shown.