What would cause a loss of water pressure in the hot water faucets, throughout the house, after the installation of a new hot water heater?

A few things... start at the beginning. What kind of pipe did you use? Did you reduce the pipe size.. It could be the shutoff you used to shut off the cold water to the water heater. Did you use copper fittings.. If you did... did you solder the pipes in place on top of the nipples extending from the water heater? This could collapse the cold water dip tube and reduce water volume as you suggest.

I guess first, check the flow of water out of the tank at the drawoff of the heater... here, hook up hose (leave cold water flow on full) and open full and see if you get good volume/pressure. If you do then may be a problem more closely associated with the hot water outlet. If you do not have good pressure, shut cold water inlet and cut cold water pipe just below the shut off and again... check for full volume/pressure, etc. Sometimes old shutoffs look open but they are not open... some shutoffs are what they refer to as gate valves and you would need to turn the handle like 15 times to fully open this valve... so check that, too.

Again, if copper pipe... could you have soldered a joint... too much?
Any shutoffs that come out of hot water line?. these could be plugged with solder... sediment, etc.

You will need to disconnect things a step at a time and see where the problem is... this happens more frequently then you might think!

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