Many consider taping to be dangerous and I have found it is both controversial and effective. The concept is to seal the lips to prevent air from escaping. It is not to keep the mouth closed. The tape I recommend is any tape intended for application to human skin. Why? because those tapes are the least likely to cause skin irritation. I am personally an advocate of taping.
Other solutions
Mouth Breathing is when you open your mouth and the air pressure from your PAP is venting out your mouth typically showing on your charts as a large leak which can substantially negate the effectiveness of your therapy. It is generally not good. The solution varies depending on the person
With SleepyHead look at your Leak Rate graph where it is shaded (large leak/ LL), flat tops on this graph suggest mouth breathing. In SleepyHead right click on the left header of the Leak Rate graph and click on Dotted Lines then select "Leak Rate Upper Threshold" to get a line across the graph for ResMed. Manually set the value for Philips Respironics. Severity depends on how much over this threshold and for how long it is in the Large Leak territory.
How to manage Mouth Breathing, not in any particular order.
Tongue Trick. Place the tongue on the roof of the mouth, Practice during the daytime. The idea is to train the tongue that this is a good place to be, not overnight, but it works for some.
Cervical Collar. A "soft" Cervical Collar. This helps support and align the neck and keeps the jaw/mouth from dropping. This is becoming a very popular option. Rarely used prior to mid 2016. Users are posting a high success rate with this device. When OA tends to occur in clusters at different times of night. It's an indication that an obstruction may have occurred when the chin tucks towards the chest. It's common, and the solution is either an ergonomic pillow or soft cervical collar that prevents the neck and head from being out of alignment and cutting off the airway, but they can be comfortable, prevent leaks and prevent an airway from closing up due to tucking your chin to chest and other issues.
Fit: You are looking for a comfortable fit 2-inches larger than the circumference of your neck and just tall enough to support the jaw when your head falls out of alignment (measure your neck from collarbone to jaw and subtract 1".
It's a very small investment that has worked very well for some people. More pressure may solve the obstruction, or it might go away with positional therapy.
Chin Strap. A chin strap is to manage mouth leaks from a variety of causes. Most result from the jaw dropping or opening either partially or wider. The chin strap is to gently keep the jaw closed. If you have to crank it shut to make it work this is not the correct solution. Note that your jaw is strong enough to open if it wants to. There is one chinstrap that is notably different than others, the Ultimate Chinstrap, Search for it if you desire.
Ergonomic Pillow or CPAP Pillow, The purpose being to maintain a proper head and neck alignment while allowing for the mask maintaing the seal in multiple positions.
Mouth Guard The concept here is a closed mouth guard to keep the air from leaking out.
Taping. Definitely the most controversial. The purpose of taping is to seal the lips and prevent mouth leaks / mouth breathing. It is not to stop the mouth from opening. I make sure that I can easily open my mouth, when taped, if I need to.
FFM – Full Face Mask or Hybrid Mask. This is a very traditional solution and it is generally effective.
Dry mouth is a symptom mouth breathing that is uncomfortable. It can and does occur with some users of a Full Face Mask.
Many users use a product called Biotene to get relief from this symptom.