Natural water sources were never really safe. What bears do in the woods, beaver fever (also known as giardia), naturally occurring alkali and arsenic, there are even some plants that can poison water in some rare situations. Point being that you can't assume the water is safe to start with.
Then you add humanity, leaking septic tanks, people squatting in the woods. Things get worse if those people are maintaining a golf course, grassy areas, growing crops with lavish applications of fungicides, herbicides, insecticides, fertilizers. But on top of this you can stack the abominable behaviors of country gear-heads dumping their used motor oil, agricultural and industrial dumping, general human carelessness and callousness.
But even that may be just the start. Consider the standing water in Haiti, or Japan after the tsunami. Mama was very careful with how and where she used that insecticide. She kept is sealed in its bottle well away from hard. Them the wave came along and ground her lovely and orderly home, and that bottle of insecticide, to splinters. The answer to the question; what is in the water is like the old James Dean line. When asked what he was rebelling against he answered back 'What you got?'. Pretty much every chemical, fuel, virtually anything that could get into the water is in there in some amount.
First way to get around this is to try to find cleaner water. Any rainfall, outside that falling through smoke from fires, or vapors from the nuke plant, should be collected. Outside that careful consideration of what is in the area is helpful.
After that some mix of skimming, settling and crude filtering would be a good start. After that carbon filters would be one way to go.
The other way is what Richlacal suggests.
How about Distilling? I know the process of Distilling,Rids the water of containing Minerals,for the purpose of Purification/Clarity/Taste,When making Whiskey,Shine,etc.Does Heavy Metal Contamination Mock the same Category as Mineral Contamination?
Distillation would work well I think. I'm thinking of something like a Sierra stove. A stove that will allow you to convert the huge mounds of scrap wood into distilled water, hot food, warmth.