Trying to edit the nose, but zooming in will display the vertices behind it The first one in the clip, I can get close to the nose just fine, but the second one, if I try to zoom in... then it displays like that? 

How to fix that?

Maybe you can check what's going on, you can download it here.
Try to change the Clip Start of your scene in the 3D View Properties panel (activated with N, on the right of your 3D View window) > View > Clip > Start.