White stains & muddy deposits in stainless steel pots
Boiling water leads to evaporation, which leads to concentration of anything dissolved in the water (and there will, unless your water is distilled, always be something dissolved in it); that concentration can lead the water to be supersaturated and for trace minerals to precipitate out of solution. If you are getting water from your municipal mains, chances are it's perfectly safe either way.

The appearance of 'muddiness,' however, seems very weird to me. Water can't become muddy on its own; by 'muddy' do you mean 'cloudy'?