There probably is some dust on the mirror, and it's very unlikely that it causes visible spots. The spots you see are likely dust on the focusing screen, which you should be able to remove and blow or brush off. The mirror surface is fairly delicate, and brushing it isn't a good idea, IMO. If you decide you really need to, do it with a brush you (or anyone else) have never "petted".
The surface of the screen is delicate too, but not quite so much as the mirror. In either case, do the minimum that gets you the desired result.
A baby's ear syringe works well as a small blower for things like this.