If the coating is still basically OK, best bet is to leave well enough alone.. Do NOT attempt to "polish" a mirror, the coating is quite delicate and you risk doing more harm than good.
Mike has an article here on how to WASH a mirror
http://www.iceinspace.com.au/63-345-0-0-1-0.html
and if it was me i would do the process as he describes but leave out the cotton wool bit, just soaking and rising will probably remove almost all the dust anyway.
If the coating is damaged, then it may need recoating which can be expensive.
Malcolm