Distilled water lacks essential minerals, it will dissolve the minerals you have in you and take those, too.
Drinking it exclusively may not be the best idea.

This shows how to make a still and discusses some about distilled water.
Somewhere in this archive he has another article about distilled water that goes deeper into the pros and cons.
It's probably in one of the survivor volumes, but I forget which one, specifically.
You can down load them in pdf and likely search them for keywords.