I have a 400 gallon hot tub, use a floating bromide dispenser, but am getting a hard whitish residue buildup at the water level, and the cover is showing signs of "puckering" on the water side. The PH checks out OK, but at times it make a person cough. Any suggestions?

Take your water to a spa supply and have it tested. Or, if you have a good test kit, let us know what your test readings are. You need to know...
Bromine
PH
Alkalinity
TDS
Calcium/Hardness

It sounds like you probably have an alkalinity, and hardness, issue that is reacting with your bromine.
Al