Hi Laura, I do distill my tapwater. It is lakewater from Beaver Lake, a manmade lake in NW Arkansas. I usually have a hard residue on the bottom of the boiling pot, and this sticky red stuff that sticks to the sides. The water is wonderful though.
I have heard that sulfur water can be healthy, but I really don't know for sure. All I know is I hate the taste. My hairdresser has a salon attached to her home. Her well water is sulfur and the family cannot drink it. However, she does use the water for washing hair.
There are all kind of water here on the mountain. On one side people have iron water that leaves stains in sinks, bathtubs and toilets. You cannot wash clothes in that water and its taste will turn your stomach. Down the mountain to the north the shallow wells have natural gas bubbling into them. The water can be drunk after sitting out a day or so to let the gas evaporate out. There are stories of dropping cigarettes in the toilet and setting the water on fire (although I am not sure this is true) My house spring comes from a cave and is so hard it leaves little stalactites hanging from faucets. All of this disgusting water could be made potable with distillation.