When an infection in the sinuses spreads to the mouth, it may infect the gums and the teeth through your saliva. This infection can change the consistency of the saliva and you may develop bad breath, either all the time or just in the morning when your sinus infection is flaring. Dental decay can also occur, which may be mild but can become severe enough to rot your teeth.
Furthermore, the gums of mouth breathers are often dry, just like their chapped lips. This drying results from the dry air that you breathe
through your mouth and a change in consistency that occurs in the saliva. Dry gums can bleed and turn red around the margins of the teeth. When this condition progresses, the gums can hurt when touched and/or when you eat. In fact, a dentist once told me that people who suffer from allergies have more dental problems than those who do not. I think that he had half the story correct: People that suffer from any blockage of the nose - including those who suffer from allergies, infection, inflammation, and/or anatomically narrowed sinus passageways - can suffer from dental problems at a higher frequency than the general population.