What effect does pool chlorine in the air have on the building structure?

Not much mostly.

If there is a really high concentration, it might cause corrosion of some metals, and it might increase the perishing and cracking of plastics or Rubber over a period of some years. But for that to happen one would expect there to be careless or incompetent application of the chlorinating equipment or chemicals.

Of course, it is quite possible for people to blame the chlorine, when actually there are other chemicals around that caused the problems.