I had to clean a SRL camera mirror once. My friend changed the lens under heavy rain and water drops went into the camera. After some thought I went for a lens detergent that I knew leaves no traces (can't remember the name) and I used a couple of those cotton sticks people uses to clean their ears. Veeeery carefully I "attacked" each spot and removed it. Then I gently blew some compressed air. I don't know if it was luck in its purest form and I won't do it again unless absolutely necessary, but it worked.
I've had cause to do the same. I used a cotton bud wrapped in a well-washed micro-fibre cloth. Same result - lucky! I would only do this on a mirror which showed no signs of "peeling" though.