I'm no plumer, but I think some hot water heaters are lined with a coating or something against rust ??? Possible it's peeling off ???

I'm a retired plumber, so youre in luck, sort of.  The white material \, if it is stone-like in consistinscy, is in fact limestone, from the lime dissolved in the water.  There are availabel, electronic water softeners called de-ionizers.  Get one and install it on your incoming water line.  This removes the ionizing electron from the lime, causing it to become non-reactive.  Over time, the de-ionizer will remove scale buildup from the existing plumbing. If you call a softener dealer, they will try to talk you out of the deionizer, saying that it does not remove the limestone.  Well, no shit!  It makes the lime non-reactive.  Any plumbing supply house should be able to help you out, and any idiot can install one.

You have mail

Run 2 quarts of vinegar through the water heater
It will dissolve the mineral scale
Do a quart every 6 months

Troy:

Given the age of your house, I'll bet it's the dip tube in the water heater.  The dip tube is the plastic pipe in the water heater that carries cold water from the inlet down toward the bottom of the tank.

We lost a water heater in the 1/94 Northridge earthquake and replaced it with a gas-fired heater from State Industries.  After ~5 years, we began to notice that the aerators in the sinks were getting clogged with these fine bits of granular white debris.  They were the size and consistency of laundry detergent.  We were cleaning aerators every three days or so in the kitchen.

These white bits will not dissolve in vinegar, while white calcium deposits will dissolve.

The source of them were dip tubes from a manufacturer that chose a not-too-robust plastic for the dip tube.  This bad dip tube was sold to a number of heater manufacturers, in addition to State.  

In addition to the plastic in the aerators, we also were running out of hot water in the shower far earlier than we had before.

There was a class action settlement against the manufacturer of the dip tubes, but the enrollment closed on 1/1/2001.

The good news is that $15 and an hour's work set things right.  I replaced the standard dip tube with one from a quality manufacturer, and the problem has disappeared.

Water heater maintenance should consist of a long drain from the bottom valve (replace the stock screw valve with a full-port ball valve) every 6 months, and a new sacrificial anode every 5 years.  Keep up on these things, and a water heater will last ages.


Sean

Contact me offline with a number and time to call, if you think this is the problem, and I'll give you a ring.

I think Sears sells those fancy to not so fancy, whole house water softening units.  They look like a cross between an ice-cream maker and a water heater.  I'm sure the crack team of trained personel at Sears can answer all of your questions.  Actually, you'll probably get better advice from this gun site.  AR15.com=King of all trades.

Sean_Burke got it right.  I think it's the dip tube, too.  Calcium build up is more gradual, and usually will not keep re-clogging strainers with particulate.

Troy,

Finally some information I can send your way instead of the other way around.  Until very recently I worked in Hydronic and Domestic Hot Water Sales.  I dealt mainly in [size=6]HUGE[size=6] hot water systems for tall buildings, schools and industries, but also many smaller residential units too.
   I would agree with Sean_Burke to start.  The dip tube will cost you only $15 or so and about an hour of your time to install.  If that solves your problem then your done.  If not, it probably is a calcium build up issue.
    Water from different sources, even in the same locales, can be very different in terms of hardness.  The harder the water the faster calcium deposits will build up.  The heating of water "cooks" these mineral salts out of solution.  They end up piling up at the bottom of the water heater and to a lesser extent get deposited throughout your plumbing system.  

Symptoms:
> Not getting as much "shower time" as you used to.
> The water is not as hot as before or you have to turn up the thermostat on the water heater.
> The water heater takes longer to reheat the water after being used up.

If these are your problems you may end up installing a new heater.  Residential units don't really have a viable means to remove the build up.  You could try flushing some of it out via the drain fitting, but that is not likely to help if it has not been a routine part of your maintenance.  You would be shocked to find how much calcium can build up inside a heater.  ( It is not unusual to have workers spend hours shoveling calcium deposits by the wheel barrow out of large commercial units. )

If you need to replace the heater you should have your water's hardness checked.  If it turns out you have hard water I would recommend installing a softener on the incoming supply.  Not only will that prolong the life of the new heater but will save you money by reducing the amount of laundry detergent and dish soap you use.

I will keep my fingers crossed that all you need is the dip tube.  Good Luck