Health
Rodents hide illness well. By the time something is obvious, it is usually already advanced.
What to watch
Laboured or clicking breathing, a hunched posture, fur that stops looking groomed, sudden weight loss, or reluctance to move. Any of these justify a call to a vet who sees small mammals.
Red staining is not blood
Rats and mice secrete a reddish substance called porphyrin around eyes and nose. A little is normal; a lot usually signals stress or illness rather than injury.
Lumps
Mammary and other tumours are common, particularly in older female rats. Many are treatable when found early, which is a good reason to handle your animals regularly enough to notice changes.