Distilled water is okay - some would even say preferable - if you're brewing extract based beers. If you're mashing, then you should not use distilled water. Rule of thumb is if your municipal water is good to drink, then it should make good beer. One of the most common issues with municipal water is chlorine/chloramine. If your water tastes even just a little "chlorine-y," this can get magnified during the fermentation process, producing medicinal off-flavors. The traditional method of removing chlorine by boiling the water or letting it stand overnight will not remove chloramine, which is the preferred disinfectant for many municipal water sources. Both chlorine and chloramine can be removed by carbon filters (including Pur, Brita, etc.) and Campden tablets.
"Chill haze is not a flaw."
Supersecret sour beer experiment
Battle Cruise Blonde Ale II