Sounds like, for the car, a similar problem to Lithium. I think Lithium is a pretty common element, as is carbon, but apparently getting either in a form to make a battery is expensive. Otherwise, I assume, electric vehicles would be using something like Saphion LiIon.
Not sure about his harping on "integrated devices". Lost power between components of a tube TV set is hardly a defining characteristic of them, and as far as I know the problem with separators in other batteries is not a matter of efficiency (failure, rather, is the problem).
For cars I can't but imagine some form of hydrogen, either the gas or a hydrocarbon like alcohol, is the better way to move such large quantities of energy around. But, for medical or small electronics, sure, an improvement over Lithium would be great.
Though, I _really_ hate the practice of embedding custom hard-to-replace batteries rather than using standard, replaceable, ones. I can see how aesthetics drove that decision for the iPod, but my new cordless mouse has one, whereas its cousin, the logitech MX610, uses two AAs.
Bit premature to talk about that as regards paper batteries, though. That's marketing, not chemistry.