There have been no studies establishing serious long-term dental problems arising from wearing face masks.
Wearing a mask for hours daily can lead to dehydration, as many people breathe through their mouths, not their noses, while wearing the protective covering. Dehydration can lead to bad breath. Hence "mask mouth" is a new nickname for bad breath caused by prolonged mask wearing. Dehydration potentially can contribute to cavities and gum disease, but there is no evidence on that point.
The Centers for Disease Control recommends that anyone wearing personal protective equipment for long periods of time (namely health-care workers) drinks plenty of water and takes scheduled breaks when protective gear can be safely removed.