I would never use the tap water again! I've ruined my mirror doing just that and had to re-coat it afterwards. I believe that the problem is in the chlorine, used for water treatment, which is eating aluminum aggressively (see the video).
On several forums and web sites there are plenty of recommendations involving use of your bare hands, mild dishwasher detergent, and tap water for deep cleaning of the primary mirror. I'm telling you - it's not good for your mirror!
That's right, the mirror's aluminum coating is covered with a good protective layer of silicone dioxide, which is chemically inert. However if that cover is not consistent enough, or you have a tiny scratch in it, the chlorine from tap water will find it's way to the aluminum atoms and dissolves them through and even under the protective coating, leaving transparent holes and white residue around them as it happened with my old mirror.
Yes, some people are using their tap water without any problems. I believe they are just lucky to live in places where the water treatment plant uses a different chemicals (or methods) for killing pathogens in the water. Or they might have their own in house filtering system, effectively dissipating chlorine, or thir protective coating is still good enough to shield from elements.
Anyhow, to be on the safe side, the best option is to spend some money on a couple of bottles of 90% alcohol or mineral spirit. Or to use the distilled water. Also I don't like the "bare hand massaging" technics which is often recommended either. A single tiny but hard particle under your hand can scratch the mirror badly enough. The best option I know about - is cotton balls freely floating over the submerged mirror surface. Move them by rocking the vessel with the mirror covered in alcohol.
By the way, I had my 12" mirror re-coated last weekend at the famous Bob Fies home lab, which is used by John Dobson of the Sidewalk Astronomers for many years. I'm going to share my experience with that soon.
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