Mesh is on the inside of the object in certain areas? When I am zoomed in on the object the mesh seems to go inside of the object.  



In a more zoomed out view you can start to see the mesh again.
I have changed the 'start' clipping distance to 0.001, however this doesn't seem to affect it very much.
What am I doing wrong?



Here is the file:
It looks like you've got a subsurf modifier enabled. You can disable it in edit mode so that the subdivided mesh doesn't block you from seeing the wireframe.