It's funny I've heard the saying "close your mouth or you'll catch flies". I never really thought that keeping your mouth closed would have medical implications. Perhaps if you were a member of the mob. Now that I am a dentist I realize that mouth breathers usually have permanent gingivitis.While this is not as bad as it sounds it still gives the person red and bleeding gums. This is the extent to which I was taught mouth breathing affected people.
It now seems that mouth breathing has other and more serious considerations. There is a strong correlation between breathing rate and a number of diseases Asthma being one. It also has effects on posture- the head and neck are extended creating muscle stress. The abdomen and diaphragm are impacted. Which causes a loss of muscle strength. There is Long Face syndrome which is pretty much what the name implies... a long face which was thought to be genetic but the culprit is mouth breathing. It also turns out that nasal (through the nose) breathing supplies more oxygen to the blood than mouth breathing. This is a brief overview a more indepth analysis of breathing is found by reading Patrick McKeown and the seminal works of Konstantin Buteyko.