Same problem but in spades. Using the wire charger it charges slowly, but something is clearly eating power since it went from 45% to 19% in a single hour just running New York Times. Plugged it into a charger with an indicator light and it flashes, so sometimes it's receiving charge and sometimes it isn't. Battery Widget (I forget its name) shows the same thing--sometimes it's receiving charge and sometimes it's discharging, making for a net slow charge.
It's dead now, and will be posted to Seoul for a proper fix tonight. Curse this Lollipop--I'm traveling Friday and really wanted it along.