Background: I was diagnosed with obstructive sleep apnea some years ago, and I've been sleeping with a CPAP device ever since. In general, CPAP follow-up and compliance rates are pretty terrible. Thankfully there's a very helpful community out there to help people with their various issues (reddit, apnea board, etc). I've basically tried everything and I've spoken to countless of people in the same boat. I'm just a guy on the internet, so take what I'm saying with a generous pinch of salt.

One of the most common issues with snorers and apnics (is that a word?) alike, is that things get worse when the mouth is open. When you're on nasal CPAP, opening your mouth will cause a lot of the air to simply blow out your mouth, which will reduce your effective therapeutic pressure (i.e., CPAP is now practically useless). If you're using a full face mask, an open mouth can reduce the fit of the mask, allowing escape, usually near the chin. This, too, can result in a drop in pressure, though usually not as dramatic as with a nasal mask.

There are basically zero good ways of preventing your mouth from opening at night. It happens to some people, not to others. No clue why. If it happens to you, nearly every "solution" sucks. Chin straps don't work, they will make your apnea worse by pulling your jaw into your airway, exactly where it's not supposed to be. Cervical collars are incredibly uncomfortable for sleeping. Mouthguards (like the kinds boxers use) are really uncomfortable for some people, but some people seem to tolerate them well enough.

On to the tape: there's only one reason to use it: to keep your mouth shut at night. Mouth breathing = bad. Especially when on nasal CPAP. Use a low-stick tape that's skin safe. I use a piece roughly the size of a Charlie Chaplin moustache. That's wide enough to keep my mouth shut, and narrow enough so that I can still breathe out of the corners of my mouth if I really have to. I do occasionally suffer a corner-of mouth-leak, but as it's a narrow gap, the CPAP machine can easily cope.

A word on aspirating vomit, as this seems to be a common concern. If you suffer from awful reflux, or are just unlucky enough to have to throw up while asleep, you're going to be having a bad time. Regardless of anything else. If you're on CPAP, there's a chance the pressure will be sending bits of goop down your airway. This is bad. If you're wearing a mouthguard, this will be worse. If you've taped your mouth, this too could make things worse. I once had threw up while on CPAP and mouth tape. Nothing bad happened, when the process started, it startled me and woke me up, I instinctively removed the tape and the CPAP mask before the vomit reached my mouth. Not fun, but no damage either.