Distilled water, if left in the open, becomes acidic (it actively absorbs anything around it, primarily carbon dioxide). This is not a great concern, neither is the fact that it *will* leech some minerals and salts from your body.
A good alternative is carbon-filtered water, if you can get a cheap carbon filter. Breta-filtered (or similar) is another good option, as is bottled water (some worry about plastic in the water though, I doubt it's a concern).
Long story short: You probably shouldn't drink tap water. Fluoride and Chlorine aren't good for you.