Dwarves already have a hidden 'dirtiness' meter. This, as it increases, increases the risk of infected wounds.
Introducing a risk of diseases would add another element of !Fun!. Proper prevention of miasma and (maybe) avoiding rotting zombies, etc, due to a chance of disease would become more important. Suppressing vermin becomes more important - so breed more cats or trappers. I believe it would make a deeper game, without too much effort and another strategic element. Plagues could shape the game world, adding a new element of chance.
Obviously, most diseases would be minor, only causing a rash or something - a minor illness. But the risk remains of a ore deadly disease. It is likely diseases could be completely controlled with proper care, as having you legendary weaponsmith die suddenly from lung-rot could be the wrong kind of fun.
As a consequence, dwarves could try to get a bath - maybe once a year or something. They would get a unhappy thought if they were unable to have a bath at all. They could bathe in a stream, etc, for a tiny decrease in happiness, but a moderate increase in cleanliness (like drinking water happiness wise.). You could fill a pond and designate it as bathing, and this would have a higher happiness boost. And finally, baths out of metal or stone could be built and assigned to dwarves, for a larger boost to happiness. Using soap would increase the boost to cleanliness and happiness.
So what do you guys think?