Distilled water, which is what you're talking about, is pure water and there's nothing wrong or unhealthful about drinking it. Trace minerals contained in regular well or lake water (or where ever your tap water supply comes from) are so insignificant in quantity that your body would never miss them as a nutritional source, and are all contained in much larger amounts in food.
Distilled water, sold in 1 gallon jugs in the store even today, originally served two markets. First, irons, (as in ironing clothes) would eventually clog with calcium build up if distilled water where not used. Those were the days when people spent money on something, they treated it with care and expected it to last, unlike today's throwaway, "I'll just buy another one," society.
Calcium scale in certain small appliances can sometimes be easily neutralized with an occasional rinsing or cycling through (as in a coffee pot) with hot vinegar.
The second reason for distilled water was for baby formula. It prevented certain stomach ailments or distress in young, sensitive stomachs. Certain parts of the country has better water quality or higher mineral concentrations than other parts. Sulfur dioxide (stinky swamp gas) can be found in a lot of wells around the country, and can upset some baby's and children's digestion.
So, don't be afraid of using or drinking distilled water.
