The goal is not, apparently, to make a huge one and power it with a lake of blood from conquered human victims, but rather to help power medical implants. The papery nature of the batteries means they could be printed in sheets and easily cut to the size and shape needed for the patient. Then, once the thing is drawing juice from your natural fluids, you don't have to worry about changing the battery. It also seems like you could replace the mat in a UFC ring with this stuff and power the whole stadium with the sweat and blood from fighters, but we haven't heard of any prototypes for that yet.
Apparently broken teeth short circuit the whole thing.
By the way, as creepy as this seems, it's still less hardcore than the old way of powering devices like pacemakers: they used to use nuclear power. They would have a little hunk of plutonium inside the battery, and as it decayed, it released enough heat to power the device. Whenever a patient passed away, they'd have to ship her freaking pacemaker to Los Alamos to safely dispose of the nuclear material inside.
"Should you worry about the radioactivity? I wouldn't say so. Not with a heart like that."