Very quick math says this is much weaker than a potato battery, which is a fun comparison. [1] puts the capacity of a potato around 0.1 Wh, quite impressive. Using the numbers from TFA I get a capacity of 5.2 µWh [2]. For reference an AA battery is 4.275 Wh.
A spent potato battery is apparently not edible, but 5.2 µWh does not provide much power. Also a potato battery is not rechargeable, while this one is, if you do not eat it of course.
It's also plainly true that any battery with too much power, when bitten and chewed, would form lots of electrical shorts in your mouth and burn the hell out of your insides.
This thread seems to be essentially all wrong.
"What does this do to its edibility once the energy has been all used up? "
The energy used to run the clock doesn't came from the potato. It comes from the coal used to smelt the zinc from its ore.
"Not sure how it will taste, but it will reduce the ascorbic acid content."
Probably true, but not a big deal
"Potatoes have a higher content of vitamin C than even oranges do."
Not true
http://en.wikipedia.org/wiki/Vitamin_C#Plant_sources
"You will also get some metal ions in your potato.
Copper ions, zinc ions, etc, depending on what your electrodes are."
Not quite true, there's no "probably" about it. The energy is released by the conversion of metallic zinc to zinc ions.
"Perhaps some organometallic compounds."
I doubt it; most organozinc compounds are not stable in the presence of air or water.
"Some of the metal ions may in fact be vitamins"
No, they may be minerals which the body uses, but they can't be vitamins since ther are not organic compounds.
A spent potato battery is apparently not edible, but 5.2 µWh does not provide much power. Also a potato battery is not rechargeable, while this one is, if you do not eat it of course.
[1] https://sciencing.com/make-potato-battery-6537882.html - 0.5V * 10mA * 20 h
[2] 0.65V * 48 µA * 1/6 h (you get a 10 min runtime at the wattage)
P.S. I know this should be calculated in joules, but battery capacity is always listed in (k)Wh or mAh, so I kept to these units
edit: correct potato capacity calculation, was off by a factor of 10