My belief is the reason that a small amount of air left in the turkey bag is not a problem is that it will quickly be displaced and flushed out of the bottom of the bag along with the CO2 being exhaled by the continuous flow of inert gas, but it is easy to remove nearly all air from the bag by first collapsing the bag with the open end around the forehead as described in the PPeH. The last remaining air can then be sucked out using the tubing before attaching it to the flowmeter regulator.
I believe that air leaking between a mask and the face is more of a problem because it may continue to leak and be breathed even after the inert gas begins to flow. Exit International doesn't recommend using any type of mask for this reason. The Wikipedia page for the nonrebreather mask says that because they are one size fits all, there is a possibility of air leaking through gaps with the face. I believe because the inert gas flows into a bag reservoir, it isn't designed to have a pressurized outflow of gas between the mask and face, so air would not be prevented from entering through any gaps with the face as it would if there were an outward flow of inert gas. Another concern is even if the mask fits perfectly while conscious, the face shape may change after unconsciousness due to muscle relaxation, resulting in gaps with the mask. For these reasons, I would not consider using any type of mask myself. I don't have any medical expertise, so I choose to follow the recommendations of Exit International based on their reported years of experience using the turkey bag with adjustable elastic. I believe although the turkey bag seems inelegant, improvised, not "cool", etc., there are very valid reasons to believe that it is much more reliable than any type of mask. These are my opinions and everyone is free to choose for themselves.
The PPeH says the gas must contain less than 2% oxygen to be effective, so yes, even small amounts of fresh air entering the mask could create problems.