I would recommend better ventilation and air filtering if you have stagnant air with an indoor pool. I don’t know enough to speak to what it will or won’t do for the pool water but I do know something about other air issues. Indoor air quality is one of the design principles for rating environmentally friendly building construction (part of what I do during normal work back home). While we focus a lot on VOCs, we also look at mold (which loves high humidity and stagnant air) and other chemical off-gassing and pollutants. There are significant problems that can result from poor indoor air quality. As Zea said, it can aggravate asthma. It can contribute to nausea, eye irritation, headaches, rashes, and allergic reactions. Studies routinely show that poor indoor air quality leads to more sick days. Over time, excessive exposure to air pollutants and chemicals can lead to more serious health problems.
I’m not trying to come off as frightening or preachy, just want to pass along some knowledge. Every situation is different and you don’t have to have a tornado to avoid stagnant air. To ‘fix’ indoor air problems you can address: 1. Source, 2. Ventilation, 3. Air cleaning (filtering), or 4. Exposure. The source being the pool and the chemicals used there; not much you can do here other than keep a good chemical balance (TFPC

) and look at where you store chemicals. Ventilation usually means increasing the amount of outside (clean) air you bring in and/or improving air distribution. The downside to this in an area like Denver can be increased heating bills in the winter but better distribution alone can do a lot (think about how the returns circulate the water in the pool and avoiding ‘dead’ spots, sometimes just changing an angle can make a big difference). Air filtering can be as simple as installing a HEPA or a higher MERV filter (you may have to change it more often but, IMHO, it is worth it). Exposure is simply how much time you spend in that air.
For a home I would make sure I had good diffusers, use a better filter, and consider increasing the ventilation in that area.
Anyhow, not really what you were asking for so I’ll get off my soapbox now. Sorry for the wall of text and I hope everything goes well for you.