According to Mary Roach in Packing For Mars, there are always fans running in the ISS to prevent bubbles of CO2 from forming around astronauts. Is this true? Could this be an issue?
For the flag? Not during the spacewalk, for obvious reasons.
As an unrelated question, "bubble" is probably a misleading word, but the lack of natural convection could indeed lead to a still astronaut developing a region of high CO2 around them. It could also lead to uncomfortable increases in temperature around the astronaut, or incidents like a piece of overheating electronics going unnoticed until it starts a fire, rather than being discovered by its odor. Establishing an overall circulation pattern also tends to collect small items in predictable locations.
Anyway, going back and watching the video...the tether's obviously stiff and springy, the clasps at the ends jiggle and slide around without any evidence of damping by water drag, various small straps tend to project out at the same direction from the astronaut independent of their orientation, the flag flops around, sometimes flying ahead of the stick it's attached to and clearly not being dragged through water, the person doing the EVA several times ends up drifting around a pivot, clearly not settling to an equilibrium position due to imperfect neutral buoyancy or being slowed by water drag...
It also looks largely lit by indirect light from the Earth. You can see parts of the suit go into direct sunlight a few times later on, and it saturates the camera. Indirect light from Earth, the big blue object in the background, will be tinted blue. Color balancing the video to make the white suit and spacecraft look white will make the Earth look faded. Readjusting the balance to make Earth blue will make white things lit by that blue light also appear blue. It looks exactly as it should under those lighting conditions, and certainly isn't evidence of a hoax.
It doesn't look one bit like it's under water. It doesn't make sense for them to fake it. There is no reason to think they couldn't have the capabilities they claim, they are in fact in a better position to achieve those capabilities than we were when we did our first spacewalks. There is just no reason whatsoever to think this was faked.