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The only problem he can have from mouse feces is a type of intestinal parasite, Hymenolepsis nana.
However, if the feces are also contaminated with urine (which they likely are), I would be concerned with a bacteria called leptospirosis and several viruses such as lymphocytic choriomeningitis, and hantavirus. Infection in dogs and cats with these viruses hasn't been documented to my knowledge, but leptospirosis can cause serious liver and kidney problems.
I would inform your vet of this possibility, as well as your own physician as leptospirosis can affect humans as well. Most dogs will not develop the disease even after exposure, but the treatment is simply amoxicillin. If any clinical signs of a urinary problem or any other change in appetite, appearance or behavior, I would take him to your vet for testing.
Dilute bleach should be sufficient to clean your garage.
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