We have an ongoing problem in our hot water lines that affects all outlets, some more than others. Apparently, some sort of deposit fills up all our faucets, showers, etc. We first began to notice this after we replaced our old hot water heater. Initially we thought some sediment, or even pieces of liner from the old heater were in our hot water system. After a few years of cleaning out faucets and no hot water in the washing machine, we began to think back, and realized we never had any trouble until the NEW water heater was installed. Is there any way to check the water heater to see if it is disintegrating internally, and passing smooth, gray, chunky little particles into our hot water system? What else could we check?

You will get mineral buildup in your heater unless you flush it out on a regular basis. That plus disturbing the minerals that have already built up in the pipes when you installed the new heater has clogged the hot water system. You will have to open up the faucets and flush out the pipes again. And if you don't run monthly maintenance the new heater let me show you how.
For long life and fewer troubles you should keep your heater clear of mineral build-up by flushing on a regular schedule. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) followed by white or yellow grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. Now flush out your hot water lines on ALL fixtures that are affected . Now pull each aerator and clean the screens. Be sure you put them back togather the same way you took them out. Don't forget to flush it out every month. Your heater will thank you for it. Hope this helps, Tom