I think everyone know this fact that Mouth breathing is not the optimal way to breathe because it can affect the oxygen concentration in the blood and especially supply to the brain.
Mouth Breathing makes your head tilt forward in order to compensate for air to enter into lungs which makes neck muscles to work harder and become more stiff. These faulty pattern and over activation of neck muscles by lifting the head up towards ceiling during strenuous exercises like Deadlifts and Squats impact your performance and exercise capacity in long run.
People breathing through mouth are more stressed and have harder time to relax because of Sympathetic nervous activation.
Actually mouth breathing was meant for emergency functions during the time of battle, fighting or hunting period. Mouth breathing is active breathing and requires accessory muscles while Nose breathing is a passive and requires only diaphragm to pull air deep into all the 3 lobes of lungs.
There are two ways described by Posturepro to change this pattern:
Promoting Nasal breathing by holding the water in mouth throughout the training
Lifting the Tongue to palate for 3-5 mins everyday