I've only had to clean a mirror once, and I used one of those Zeiss lens wipes, which are moistened with their cleaning fluid. I tore it in half and wrapped it around a q-tip. After gently rubbing for a few seconds, it dries up quickly, and anything left behind will usually easily blow away. These things are handy for all things photographic, (and my wife pinches them to clean her glasses), and I keep some in my camera bag all the time. Once, somebody standing beside me popped open a can of Coke and a bit sprayed on my UV filter. Grabbed one of those little wipes, and that sugary stuff was gone in no time.
Unfortunately, on any website, you will get the occasional person who is habitually rude. Ignore them.