Flaws
Due to improper production, handling or storage, there are a fair amount of things that can go wrong with wine--most of which should be cause to return a wine if ordering in a restaurant. Some wine merchants will also take back a flawed wine, though I suspect only for their best customers.
How often a wine is flawed turns out to be a controversial questions. Some people feel that 1 out of every 12 wines they consume is flawed. Personally, I don't find anywhere near that many wines to be a problem (but then I don't have the wherewithall to consume a lot of really old wine).
A good number of people, when faced with a bottle that doesn't seem right (or is just plain awful) will say that it is "corked." They have come to use the term as a catch-all for all flaws. So just what is a corked wine?
To me corked wine has the flavor of wet, musty cardboard. Once you have really tasted a corked wine, you'll know what it is--it is not subtle. It is caused by trichloranisol [(TCA) 2,4,6], a compound released by molds that can infest the bark from which corks are made. One theory: you can't get TCA without chlorine, which is used to bleach corks (for aesthetic reasons). If corks aren't properly rinsed and dried this problem can occur.
If you haven't been "lucky" enough to experience a corked wine (at least for educational purposes), apparently you can buy the odor of the stuff from enterprising entrepreneurs. One advertised business is: The Wine Trader, attn: "Corky," P.O. Box 1598, Carson City, Nevada 89702.
Other Flaws
While some people attribute all flawed bottles to being corked, there are a number of other things that can go wrong. A non-exhaustive list follows.
There are long lists of flaws and descriptions in How to Test and Improve Your Wine Judging Ability (see BOOKS section), and Elements of Wine Tasting (American Wine Society Manual #11).
Something that probably isn't a flaw are tiny glass like crystals on the bottom of the cork (or sometimes in the wine). Assuming they really aren't glass from the winery, they probably the result of tartaric acid in the form of potassium bitartrate (cream of tartar). I'm told that this is tasteless and harmless. I've seem them and they haven't hurt me!
A final note about flawed wines. If you are on good terms with the store or winery from whom you purchased the wine, they will often replace a bottle which is flawed. No harm in trying!