Pesonally I would not ue acetone, reason is that it is a fairly strong solvent and I have lost a couple of items - none astro or glass etc - when I tried it. Have used acetone a few times and for a mirror it would be a last resort. Too many things have gone wrong.
I cannot see why it would not work, but there exists the chance that you could clean the mirror and get more off then expected. Any pinholes in the coating will allow acetone through. The coating will I expect be SiO2 so acetone should not directly harm it. SiO2 being basically glass. If you have marks then what are they from. If "dirt" then gently wet them and keep them wet for a while to loosen whatever is there.
Are the marks caused by pin holes in the coating and so oxidisation of the aluminium reflection surface? If so acetone will get at the aluminium by the same method.
Keep it off your hands, it being a good solvent will take all the oils etc from your fingers. don't sit above the fumes as you will breathe them in and I suppose could pass out - like ether on a cloth idea. Acetone is not uncommon, women use it to remove nail varnish - that is the easy way to buy it in small amounts, ask at the cosmetics section of a supermarket. I used it for rod (fishing) building - to clean surfaces and clean up the assorted mess I would create on the blank.
Concerning its strength it will clean off a set 2 part epoxy varnish on a rod. So consider thgat the rod coating is intended for 5 to 10 years outdoor use at the sea in all weathers, and acetone removes that fairly easy. Not tried but I think it will dissolve Areldite epoxy glue.
People (and I) have used IPA. Seems a bit less aggressive. It is said it doesn't leave a deposit but I have always had to clean and "polish" anything I have used it on afterwards.
I would identify whatever the marks are first.