Is the sediment that is clogging my kitchen and bathroom faucets making the water in my home unsafe to drink, bathe or brush my teeth with?

It depends on the level of sediment and the type of material it is made up of. Call your local water authority and tell them to come test the water.

As a rule sediment will consist of Calcium Carbonate and Iron oxide, traces of sulfer or other minerals. Nobodys died from them yet and they have been in water since we started to drink it. Regards, Tom

You have gotten two good answers. Some sediment could be harmful but like Static says you need to have a water test. The most common minerals in water are actually beneficial to your body. I think we are assuming you actaully mean minerals and not sediment which would be very large particles that settle in your water heater andtubs.