I've been told that water-heaters build up sediment at the bottom over time, and should be flushed out (ie. drained, then allowed to refill). Is there value in this exercise? Does that value exceed the cost of the hot water lost in the process?
It's part of the recommended maintenance for the heater, so there's definitely value in it. No matter how clean your water supply, there's always going to be some amount of sediment getting through, sand and grit or dissolved minerals. As the water sits in the heater's tank, that can settle out and build up on the bottom of the tank.
How much does it cost to heat a 50gal water tank from the temperature the of the water mains? 50gal = 50*3.785 = 189.25 L. Specific heat of water is 4.186 J/g/°C, so it will take 4.186 * 1000 * 189.25 = 792.2 kJ to raise all the water in the tank by 1°C. Assume the water comes in at 50°F/10°C and your water heater is set for 150°F/66°C, so you need 792.2 * 56 = 44.363 MJ. One unit or kWh of electricity has 3.6 MJ and electric water heaters are around 90% efficient these days, so you need about 13.5 kWh to heat the water to your set point.
In my area, electricity costs are about 10¢/kWh, so it would cost about $1.35 to flush and reheat the water tank. You only need to do it about once a year (and you could maybe get away with doing it less often if you had very clean water and lived in a soft-water area). Over the life of a water heater, you're looking at less than $20; compare that with the $100s that a new water heater costs.
Besides, won't you feel better knowing you don't have all that gunk in the bottom of your water heater? :)