What would the percentage of an air/water mixture have to be such that you would be able to breath bubbles rising up, or alternatively, if the percentage is too low, that the water coming downward would allow enough air to percolate through to your mouth (downward pointing so as to avoid water coming into it?)
In theory, you can breathe plain old water. If you can breathe it in, it will fill your lungs and they will continue to extract oxygen and dump CO2. The problem is that the O2 saturation of water is lower than it is in air, so you’d need to move much more water through your lungs–and the water is so much heavier that the effort is exhausting.
So the answer is that you could in theory breathe plain water, and any amount of air in the water would make it (marginally) easier to do.
Cite please?
If I can WAG, I think the problem with this scenario is not the oxygen percent, but that our lungs are not designed for liquid filtration, meaning that even if we could magically drink liquid oxygen and not freeze, we would still suffocate.
Of course, you know, this may call for experimentation 
Actually, it is possible for mammals to breathe liquid. Did you ever see The Abyss? The characters in that movie use a fictional liquid breathing apparatus, but during the film a rat is shown actually breathing liquid. Here’s a link to the Wikipedia article on Liquid breathing. It has not been tested on humans because of some problems that have not been resolved, but it’s still a facinating idea.
–FCOD
I kind of get where where you are going here. But I don’t think your breathing a water/air mix when you do that, your actaully extracting the air out of the water before it goes down your windpipe. It’s probably more a matter of the rate of air bubbles through the water than a % mix.
If you’ve ever been scuba diving you can take you regualtor out of your mouth while underwater, hold it about a foot under your mouth, hold down the purge button to release a rapid flow of air bubbles into the water, stick your face in the bubble stream and breath easliy.
Sweet! That’s exactly the type of anecdote I was looking for! I assume that standing under a waterfall is approximately the same thing, assuming that there is enough of a break in the flow to allow air to bubble underneath and into your lungs (and you keep your head down so water doesn’t get into your mouth.)