It depends, primarily, on your water source, chipchewmunk!
If you are processing artesian well water or water from a clean spring, then my guess is that with a dash of high quality sea salt, you would still have a good (safe) quality cooking and drinking water.
On the other hand if you have tap water coming from a common big city supply usually containing chlorine and floride, and possibly some toxic minerals, then simply boiling with sea salt, and cooling might not significantly change the consistancy of the water.
Boston, for instance, just recently improved
http://www.boston.com/news/local/art...ling_with_joy/ the taste of it's water by switching from the traditional chlorination to using ozone to purify the public water suppy, so if you live in a city that has done that, it may be okay to just boil and cool your potable water.
Get a water test kit
http://www.watersafetestkits.com/ or send it to a lab
http://www.e-watertest.com/water-test-order2.html http://www.google.com/search?q=lab+t...en-US:official
and find out what's in your water if it concerns you!
Be Well.
Cool Dude