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.
I have tried the mentioned Zeiss cleaning kit for 20 bucks and itīs ok. The brush is really nice by the way. I was in need to clean one of my lenses which I was afraid to have serious damage on the front element, but it was just dirt. Now it is fine again :-)
Anyhow, I wouldnīt clean my lenses just for fun, I do it only if itīs really necessary like in this case.
Years of grime, for old uncoated lens just windex it to get the grim off, then use alcohol and lens cloth or tissue for the final cleaning. The alcohol will remove any moisture left. I yet to see hydroscopic glass.