Mice (and rats) have sometimes "unwanted tenants" in their coat.This is usually a louse, which can be seen with plain eyes. It usually dwells behind the ears and in the neck or in the armpits - in the places a mouse cannot reach itself. Take the mouse in your hand and (in good light) look at the hair roots and the skin. In light coloured mice the lice show as very small dark spots. If you look very closely, you can see these spots moving around. Lice are transmitted from one mouse to another if they are housed together, so if one mouse in a cage has lice you should treat its cagemates, too. Lice can also get transmitted through human hands. It reproduces by laying eggs in the mouse's hair. Mouse lice do not get transmitted into humans.
Information on louse treatment can be obtained from vets or very good pet shops. Ivermectin is good and reliable, but do check the correct dosage from your local vet or club.
Sometimes mice get endoparasites, which can be fatal if not treated. As with many ailments, in this case prevention is the best cure. This is, a mouse should be wormed regularly. Mice can get worms from other mice or from food collected from outside (always wash carefully all grasses etc. collected from the nature) or from dirty conditions (always remove fresh food no later than the next day).
If a mouse has worms, the symptoms are quite easy to detect; the coat becomes coarse and dull, and the mouse loses weight even if it eats properly. You should worm your mice twice a year. Information on how to do that, as well as the right medicines can be obtained from a vet. Always consult a vet before de-worming a pregnant doe. Does should be wormed before mating them.