Is there a reason to not use cheap vodka when mixing drinks?
IMHO you can’t really taste the vodka.
The classic rule is buy cheap vodka and expensive gin. Some vodkas are not very pure and you will be able to tast them. Most should be ok.
Depends on the drink. For something like a screwdriver, I think you can tell, but for something with stronger flavors, it probably doesn’t make a difference.
lee is absolutely right about the gin, though. Don’t scrimp there, because it will hurt you.
In my experience, cheap vodka can make cause milk and Bailey’s to curdle.
There are some ultra-cheap vodkas out there that are just plain nasty. The regular moderately cheap stuff should be fine for most things. Vodka is just alcohol and water (unless it is a flavored vodka).
In a blind taste test run recently by the New York Times, Smirnoff vodka was the hands down winner. It beat out a lot of ultrapremiums for taste.
I’ve known serious vodka drinkers to gravitate to it and forego Gray Goose or Belvedere.
If I were you, I’d buy a bottle of Smirnoff and mix away.
You can buy much cheaper than Smirnoff.
You can buy much more expensive than it as well. It seems a happy median and is far closer in price to the cheap stuff than the expensive stuff.
I can usually tolerate decent vodka in a mixed drink, but the cheap stuff feels like I’m drinking a glass of fire. It hurts! Once I made the mistake of ordering a 75-cent vodka and cranberry in some ratty place in Vegas, and the first (and only) sip nearly made me lose my lunch.
Life is too short to drink cheap booze. A wiser man than me first said that, and I believe him. 
There are some kinds of cheap vodka that are okay. I think I had some Popov once, and it was noticeably inferior… but it’s easily countered by simply making your drinks less strong. An acceptable detriment for the price.
When it comes to drinking vodka straight, however, I need Skyy or above… Absolut, Stoli, Ketel One…
But, ultimately, my advice is to never, EVER buy one of the $5 bottles of Albertson’s Brand or whatever you can find at the supermarket. Even diluted in one part liquor to ten parts mixer, it still tastes like shit. So if you need something cheap, at least scrounge the extra two or three dollars to get something that’s just a little beneath Smirnoff.
Go with something like Stockholm Kristal. Its only $12 for a 750ml, and still tastes decent, if price is your qualification.
I don’t drink much, but I’ve discovered that cheap vodka is a big mistake. Unless you drink it by the crate the cost difference does not even begin to make up for the taste difference. Cheap vodka can be described by how well its tolerated, not by how well it tastes.
Top shelf vodkas can be described as decidedly smooth, if not actually tasting good. And another big thing I’ve discovered. Top shelf vodka will get you just as drunk but it will not make you sick nearly as easily nor will it give you nearly as big a hangover as the cheap stuff. Really premium stuff like Stolichnaya or, IMO the best, Ketel One, won’t give you one at all (unless you go overboard).
Expensive vodka is the world’s biggest rip-off.
By law, all that can be in vodka is alcohol and water. It is dilluted alcohol. No more, no less. Even that $50.00 bottle that looks so nifty up on the shelf is nothing more than diluted alcohol. Anyone that shows off what expensive vodkas they drink- unless it’s serious stuff made the old fashioned way in the vodka drinking parts of Europe (which you can’t buy at the liquor store in fancy bottles, and which your bar doesn’t carry) is not only a show-off, but a particularly clueless one.
That said, the filtering processes do vary a bit, and it’s better to avoid the $5.00 a bottle stuff because of impurities (which, incidently can be filtered out with a carbon water filter). Once you get in to names you’ve heard of, you’re doing all right for mixed drinks, and probably for drinking straight if your in to things like drinking vodka straight.
I’m so excited- today I discovered Trader Joes sells their own brand of vodka for ten bucks for two liters. They did well with Charles Shaw wine, so I’m going to give their cheap vodka a shot (hehehe).
I can taste vodka in drinks. 
Blerghhhh.
I’ve been curious about this liquor filter which cleans up cheap booze.
To be fair, this does make a decent cleaning fluid. It can helt get the gummy stuff from labels off.
Safeway frequently has Smirnoff on sale for $8.99/750ml, and has a continuous promotion where you get 10% off any 6 bottles of spirits. If having that much liquor in the house doesn’t give you the willies, it’s a pretty sweet deal.
I find it’s best to taste a lot of things because everyone has different tastes and metabolises stuff differently. For some reason I can drink flavored Smirnoffs with no problem, but get a splitting headache from just one drink of flavored Absoluts. (Plain Absolut I have no problem with, but don’t find it any better than Smirnoff for the price. It gives me a strange drunk - sort of a smother instead of a buzz.) I like Ketel One ok, but not 250% more (which is about the price compared to Smirnoff.) I’ve had either Grey Goose or Belvedere (forget which one) and thought it actually tasted BAD. Albertson’s sells a Absolut knockoff called “SIX” which runs about $10 and is actually pretty good. I think it’s superior to Absolut, but I recently got a “bad” bottle that actually smells/tastes like dirt; don’t know how common a problem that is.
In the long run, the best vodka is what you’re used to. As you can probably guess, I drink A LOT of Smirnoff and usually don’t have any problems with it, whereas I had a couple Ketel One drinks while out a couple weeks back and they really hit me the wrong way, which never used to be a problem before. My advice is figure out how much you’re willing to spend, find a brand in that price range and learn to love it, heh heh. Both my husband’s father and his uncle were/are dedicated Popov martini drinkers. ::shudder::
I’ve found a good rule of thumb is not to buy any vodka that is made in the US but has a fake Russian name (like Ruble Vodka, which IIRC is made in Cleveland).
That would presumably not include Smirnoff, which is American vodka with a genuine Russian name.