When I replaced our primary residence water heater with a tankless, I went ahead and applied for a permit. After I finished the installation (major work, but very educational), the inspector came over and signed off the permit after looking at it for 2 minutes.
The only thing he really seemed concerned about was the pressure relief valve (which is kind of useless on a tankless, but whatever). He didn't measure or even look at the very expensive single-walled stainless-steel flue I installed, nor did he check for the mandatory 3 inches of clearance from combustibles (ok, maybe he just eye-balled it). He didn't concern himself with all the other clearances around the unit that were clearly marked on the housing. Perhaps inspectors are used to seeing some really shoddy installations and anything that even looks remotely like the installer took some care is fine with them?
Anyways, when I replaced the hot water heater in our rental condo (conventional tank), I didn't bother with a permit. Nobody at Home Depot asked for a permit or my plumber's license either! :-)