It certainly can be done at home but there are a couple of points that are good to be aware of or which can minimise the likelihood of adverse impact.
As Doug has alluded, not all mirrors are created equal. Some are much less tolerant of cleaning than others. I suspect the silvering of some ages much better than others, too, perhaps based on both the quality of the original process and the conditions in which a camera has been used and stored. I have an old Praktica here with a mirror that had clearly been around the block a few times when I acquired it, and it was decidedly the worse for wear. On the other hand, the quality of silvering used on, say, Rollei mirrors from at least the 1950s, was very good. They should of course not be cleaned more than necessary but can handle it very well if it should be absolutely necessary. So can Hassy mirrors, in my experience.
So, how do you work out if yours will disintegrate at the slightest touch, or not? Well, I'd expect a relatively modern Nikon mirror to be pretty decent but, prudence dictates that, before proceeding to the centre of the mirror surface, you carefully try one of the extreme corners, first, to test the waters as it were. If you see signs of adverse impact, you can always elect to live with the marks or have it professionally attended to, which is certainly better than trashing the mirror.
The second point is that some Japanese SLRs may have focus screens that are made of fairly soft plastics. I prefer, for the most part, to work on classic German stuff. This has its own pros and cons, but, one nice point is that many of these still had real glass focus screens and condensor lenses, and, with the usual care one doesn't have to worry too much about damaging them with various fluids, only of not scratching them.
Plastic screens on the other hand, can catch you out if Eg. you use an alcohol-based lens cleaning fluid to clean your mirror. I'll give you an example of what can go wrong. I have a few Yashica TL Electro X SLRs. One of the earlier specimens I acquired, I think the first one, had a mirror that was quite dirty because, as the mirror damping foam and/or its adhesive had contaminated it. So I thought I'd clean it. All well and good, so far.
I did a fine job of gently wiping the mirror clean with some Rosco lens cleaning tissue wadded up, a pair of tweezers, and some Rosco cleaning fluid. It was, in fact, as good as new. Unfortunately, while I was doing this, I managed to (barely) dab the tissue near a corner of its focus screen. Which went instantly opaque! And it has still has an opaque spot years later. Luckily, it wasn't in the centre of the screen, and the camera remains quite usable. But it's an enduring reminder of the need to take some care in one's choice of cleaning fluids inside a mirror box, if the SLR in question has a plastic screen. Otherwise, you may find your mirror sparkling but remain nonplussed by other signs of your presence near it, whenever you use your viewfinder!
It's up to you as to what fluid you use. If you have a very steady hand indeed, you might be happy using a conventional lens cleaning fluid to clean your mirror. But the top edge of the mirror will inevitably be situated very close to the focus screen, making it so very easy to inadvertently dab the screen. Perhaps you might elect to clean only the lower portion of the mirror, and stay well away from the top of the mirror box. I guess it depends on where the problem is?
Alternatively, you might consider a very little demineralised water as an alternative to lightly dampen your choice of cleaning material. This will be nowhere near as effective at removing skin oils or other deposits from the mirror. But equally, it's not going to hurt anything it comes into contact with. A solution might be a combination of both, possibly, (but not applied together, obviously). In any case, unless it's known for a fact that the lower surface of the focus screen is made of glass, not plastics, it is always much better to err on the side of caution with any use of cleaning fluid.
Cheers,
Brett
