Here's the forum on the Mythbusters website - has a thread about filtering cheap vodka. The show's conclusion was it can taste better but not as good as top shelf vodka.
http://community.discovery.com/eve/f...6/m/1391989528
If you mix it, it really doesn't matter. I normally drink it over the rocks and can tell a difference between some brands. But only on the first two drinks.
:edit:
After reading the thread I just cited, who knows what the hell was proven! Dang, they are all over the place on this one.