My wife noticed that my breath started smelling like mothballs or musty ... what could cause this?

Halitosis: Unpleasant mouth smell is called halitosis. Unfortunately, there is no good explanation for that. Bad teeth, throat infections, acid reflux, diverticula (pouch like lesions in the esophagus associated with food retention) have been associated with halitosis but no definite relationship found. If any of the above relate to you, then you may try to focus on eliminating those.