Oh, it's not a science fair scam - it's a great way for kids to learn about electricity! Compare it to sticking similar nails in a few other objects, and you've got yourself a poster.
But it's also not as simple as growing a field of lumpy batteries.
Huh? Reliable light is one of the best things to provide impoverished areas with, after clean water/food/medicine/sewage.
It's one of those things that we really take for granted, but if someone dropped you in the middle of the woods, I bet a headlamp and power source would be one of the first conveniences that you'd ask for.
Anyways, like others have pointed out, the energy comes from charge carriers moving between the metals stuck in the potato, not the potato itself. That particular misconception comes up surprisingly often, to the point that it's kind of a running joke in its own right. Portal 2 had a pretty tongue-in-cheek take on the gag.
But it's also not as simple as growing a field of lumpy batteries.