Fusel oils and congeners are what you're avoiding in multiple distillations.
According to The Penguin Book of Spirits and Liqueurs, "[Vodka's] low level of fusel oils and congeners — impurities that flavour spirits but that can contribute to the after-effects of heavy consumption — led to its being considered among the 'safer' spirits, though not in terms of its powers of intoxication, which, depending on strength, may be considerable."
http://en.wikipedia.org/wiki/Vodka
http://en.wikipedia.org/wiki/Fusel_oil
http://en.wikipedia.org/wiki/Congener_%28alcohol%29
According to The Penguin Book of Spirits and Liqueurs, "[Vodka's] low level of fusel oils and congeners — impurities that flavour spirits but that can contribute to the after-effects of heavy consumption — led to its being considered among the 'safer' spirits, though not in terms of its powers of intoxication, which, depending on strength, may be considerable."
http://en.wikipedia.org/wiki/Vodka
http://en.wikipedia.org/wiki/Fusel_oil
http://en.wikipedia.org/wiki/Congener_%28alcohol%29