Have a lot of black dirt and sediment coming out of water pipes. Have well water. Seems to be worse in hot water, although some faucets are getting black water in cold also. How do I know if my water heater is no good? It seems to heat water just fine.

What kind of well pump do you have?
Sediment is probably accumulating and settling to the bottom of the water heater tank. You should flush the water hearter now, even thou you don't yet know the source of the sediment.

In particular, is the pump in the well or above ground?