When you boil water, you form water vapor - water in the gas phase - as well as a mist. Water vapor is, strictly speaking, invisible because it does not absorb in the visible range to appreciable degree. The mist you see above boiling water is not water in the gas phase. It is an aerosol formed from mechanical action of bubbling (primary aerosol) as well as water vapor cooling/condensing when it hits the air (secondary aerosol).
If you put salt in water and boil the water, there is not enough heat to melt the salt. And in any case the salt is in a aqueous phase so "melting the salt" doesn't really mean a whole lot in any case. However salt can still end up in the air through primary aerosol formation - if water droplets/particles are ejected directly from the boiling solution, they will contain whatever solution was being boiled. Any secondary aersol that's formed is due to condensing water vapor, however, and these droplets cannot contain salt because there is no salt in the gas phase. I suspect that the majority of mist formed from boiling water, particularly high above the source, is due to secondary aerosol formation, but I'm not sure.