Waking up with dry mouth or throat
If you breathe through your mouth, you may wake up with a dry mouth or a sore throat. If this is the case, you can get a chin strap to help you breathe through your nose only. You may also consider getting a full face mask that covers the nose and the mouth if you cannot breathe through your nose due to chronic congestion.
Otherwise, it might have to do with the humidity. Getting a CPAP machine with a humidifier will help. Adjust the humidity settings higher and higher until you no longer wake up with a dry mouth.
Waking up with sinus congestion or pressure
Sinus congestion or pressure is probably due to your humidifier setting. Try adjusting it up or down until you find the setting that is best for you. You may even try to eliminate the humidifier altogether. If you have COPD, Chronic Bronchitis, Asthma, Chronic Rhinitis or other respiratory problems, you may find that a BiPap or Bi-level machine works better for you.
CPAP Mask is causing irritation or sores
The first thing you want to check is that you have a good fit on your mask. Make sure you purchased the right size, and adjusted it properly to your face. After that, especially if you are using nasal pillows, you may find some irritation in your nose. Try using a water-based lubricant to act as a barrier between your skin and the pillows. If this is happening after you have had the mask for a while, you may need to clean it thoroughly or replace it.
Waking up with dry eyes
Covering your eyes with an eye mask will keep your eyes protected from the air leaks and air from the machine.