I took the bathroom mirror off the exterior wall and discovered a cavity roughly 12" wide, 16" tall. I'm guessing this used to be for a small recessed medicine cabinet.
Is there a problem leaving this cavity here?
If the cavity is not insulated, your mirror will be cold and fog-up more when you take a shower. Also, if your mirror is not sealed to the wall, water vapor may enter the cavity and cause condensation and mold. If there is insulation and is sealed from water vapor, you will have no problems.
Being its an outside wall, insulation and drywall would add some energy efficiency.
In my Michigan climate, that recess would get quite cold.