It would appear that over time people have lost touch with the imperfection of natures bounty. Whilst the humble potato is a great source of complex carbs it harbours some real gotchas. The main toxin concerned is the glycoalkaloid solanine, this toxin is present in the leaves stem roots and outer few mm of the potato itself. There are many traditional steps of preparation that alleviate this concern, but the fact that in australia we sell potato skins as a pub served dish is disturbing.
Basically the way to avoid this toxin is as follows:
In relation to the pealing of potatoes the end of the peeler usually comes with a tool for taking out the eyes. I personally like perpendicular peelers for safety and comfort.
As for the greening, This is indicative of light exposure. The light exposure creates both chlorophyl and solanine in the potato on most varieties. So the greening is just an indicator that this is a risky potato. There are varieties of potato that produce solanine on light exposure but little chlorophyl, These are dangerous in shopping centres as you have no idea about solanine production levels due to fluro lights. This in my opinion means that all potatoes should be black bagged....but that is just my opinion.
This is just a summary of my limited knowledge and please take it with the understanding that I am but a humble Vegan and mostly educated in fields far from biology. I hope this is of use and welcome the input of others. I am particularly interested in the history of cultivation and varieties with different solanine potentials..cheers