Beware of green potatoes, and peel every trace of green away: that's been standard advice for decades, and for good reason. When potatoes are exposed to light, these underground tubers interpret it as a sign that they're no longer completely buried in the soil. So they produce chlorophyll pigments to help them make use of the light's energy, and they produce bitter toxins to discourage animals from eating them. The toxins, alkaloids called solanine and chaconine, are about as powerful as their better-known cousin strychnine. They apparently interfere with the structure of all our cell membranes and also with the processing of a nerve transmitter (they inhibit acetylcholinesterase), which can cause hallucinations and convulsions. Because the color change in a potato parallels its accumulation of alkaloids, greenness is used as an indicator of toxicity and therefore irreversible spoilage. It's estimated that around 15% of the US potato crop is discarded on account of greening. But until recently, there has been little careful study of the toxin levels found in typical American potato varieties exposed to the light levels in typical markets.
These findings suggest that most greened potatoes need not be discarded. But the authors make two cautionary points. Potato alkaloids at low levels may have subtle toxic effects of which we're not yet aware. And because these alkaloids remain in the bloodstream for longer than 24 hours, people who eat potatoes every day may gradually accumulate toxic levels.
So it looks as though the occasional green potato is fine, but it's still not a good idea to buy them by the bagful.
Grunenfelder, L.A. et al., J. Agric. Food Chem. 2006, 54 (16), 5847.