Sensitive test for lead in water?
I used to work in an environmental water testing laboratory.  The regulatory standard method for testing for lead in water uses an Atomic Absorption (AA) spectrophotometer.

It seems that the issue with Flint's water appears to be that the new source of water is corrosive, the water has not been treated for corrosion, and pipes in Flint are commonly made out of lead.  So if your pipes at home are made of lead and are corroding, you may have a problem that the lab at the water treatment plant was not able to test for.

If you are curious about checking your water at home, you can obtain a water testing kit from a local hardware store.  These kits come with test strips that allow you to check your water for things like nitrates, pH, alkalinity, hardness etc.  Make sure your kit allows you to test for lead.