Answer: -Greenish hunks of debris might be associated with corrosion of copper piping or fittings. That this appears at a hot water spigot might suggest interaction with copper and old galvanized piping (the hot water exacerbating corrosion more than the cold water.) If there is a possibility of this, a plumber should check things out before a more disasterous event occurs.. -Check the dip tube in your water heater. It might be falling apart. The dip tube is the tube that introduces cold water into the heater. Its purpose is to get the cold water to the bottom of the tank so that it gets heated first. Only a small number of companies make dip tubes, which they supply to all the water-heater manufacturers. One company--I forget its name at present--made a large batch of defective ones. When they come apart, they release pieces of plastic grunk into the water. If I'm right about the cause, replacing the dip tube and flushing the system will eliminate the problem.