It seems like your problem is more related to this thread: http://forums.windowscentral.com/nokia-lumia-820/205402-display-glass-different-surfaces.htmlI think my phone might be developing this issue, does seem to wipe off but not 100% completely a quick run over with your finger and they appear back. Can see me taking this back to the shop soon.
I have the same issue. Exactly the same 'foggy' patch at the top developed after about a week as in your photo, and now another larger patch at the bottom has appeared. Frustrating. Wonder if this is going to be a flaw across all of them. Getting a replacement tomorrow.