Amazing stuff. Who knows what kind of energy density can be stored?
I'd doubt very much that the liquids are totally safe. One thing about batteries is that you need elements that are reactive in nature. In the case of this liquid battery (as I understand it) the lithium is suspended in the fluid and nano devices charge the fluids to a potential, one an anode and the other a cathode. That may make one corrosive and the other acidic. It also may be that the fluids, when spilled to a ground, cause all the nano guys to stop and the fluid totally loses any potential or charge. If the last is true, I would be warning out of my a*^.