The key to good health in a mousery (of any mouse species) is keeping things clean and reacting quickly when problems arise. Mice cover their ill health as long as possible, so when symptoms are visible, you have to act fast.
Most common symptoms: apathy, lethargy, hunched position, rough hair, weight loss, sneezing or coughing.
General health info: parasites
Mouse Health Matters; A wider look at different ailments.
Spiny Mouse Health Matters; Most common problems