As in all things food and wine related, snobbery abounds here. And, as ever, it’s nonsense.
Here are some tips for cooking with wine you wouldn’t drink. They refer to wines that are imbalanced, or imperfectly made. Alas, when a wine is actually faulty (e.g. musty or just generally ‘off’ smelling or tasting), there’s not a lot you can do other than try to get your money back, or tip it down the sink. If you cook with it, you’ll likely ruin the dish.
Here are a few more minor faults (which may simply reflect personal taste) that needn’t stop you from cooking with the offending article.
Tannin
High levels of youthful or unripe tannin can make a wine unpleasant to drink (that drying, harsh sensation young reds sometimes have), but it doesn’t mean it can’t be cooked with:
Tannin doesn’t dissipate with cooking; in fact it concentrates as the liquid reduces. This could make the resulting sauce intensely astringent but usually doesn’t due to the presence of protein. Whether it’s a beef stock, a coq au vin or a Bolognaise sauce, the tannins in the wine will bind to the proteins in the food (rather than the proteins in your mouth) which will essentially neutralise their astringent effect. This is much the same process as takes place when we put milk in tea. Just don’t use highly tannic wines in low-protein foods, such as vegetarian tomato sauces.
Acid
Acidity – and sometimes very high acidity – is vital to wine. However, when it’s out of balance it can be unpleasant to drink. Here’s how to use it up:
Some acid dissipates during cooking and some doesn’t, it’s a relatively complex process that depends on the volatility of the acids present. However, I’ve found that it’s enough to know that a more acidic wine will make for a more acidic dish. So overtly acidic wines aren’t great if you’re looking for a rich and warming winter stew, but they’re fantastic if you want to cut through the richness of a butter sauce; or if you tend to finish a risotto with handfuls of butter and cheese – as I do – and you’re looking for balance.
Sweetness
White wines that are sweet without the balancing acidity can be cloying and sickly. However, paired with acidic ingredients such as tree fruits or berries, this becomes a virtue. Pears poached in a little sweet wine are a simple and delicious dessert.
High Alcohol/Cooked Flavours
Red wines that have a character of jammy sweetness due to ‘cooked’ fruit and overly high alcohol content are fine in a rich stew or braised dish; the alcohol boils away and the ‘cooked’ flavours are no longer undesirable and usually undetectable.
And finally…
Often wine is just a way of adding liquid to a dish without resorting to flavourless water. Barring a truly horrendous bottle, it’ll rarely harm what you’re cooking.
Conversely, recipes that specify Barolo, ‘a good quality Burgundy’ or decent Champagne are spouting nonsense. Adding a small amount of decent wine in the latter stages of cooking can be good, but basing a dish on a fantastically fine/expensive bottle is madness. What do you get for the small fortune you spend on a bottle of Barolo? Well, Hopefully, you get a restrained power and beguiling array of subtle aromas, all disguised by an almost frail colouration.
All of which would be lost during the cooking process.
It’s elitist nonsense. Drink the good stuff. Cook with the ‘alright’ stuff.
Wine, Food...etc 
Some very good, sensible stuff here. In fact the UK cook Prue Leith once shocked the wine world by blind testing a dish prepared with various wines and a proprietary cheap wine concentrate. Needless to say, the concentrate came top and the Chambertin performed poorly. It’s worth saying that the rule of using good wine for cooking dates from the days when half-decent wine was the exception to the rule. Dishes prepared with drinkable wine probably do taste better than ones prepared with poorer fare.
On the other hand, there probably is a logic behind using wines of the style of the ones that are traditional to the dish: inexpensive Pinot or light reds for Coq au Vin; light basic Cabernet or Merlot for Entrecôte Marchand du Vin.
Incidentally, my friend Charles Metcalfe to whom I defer on these kinds of matters believes that TCA blows off with cooking, so reckons that you can cook with corked wine. I haven’t tested this myself.
Thanks for the very thoughtful comments Robert. I totally agree that using wines of a similar style to the ones traditionally used for a given dish is a good idea. Although using a different style of wine would only usually result in a slightly different, and not necessarily worse, dish.
I haven’t experimented extensively with cooking with corked wine. Some certainly do hold that TCA blows off with cooking, but a recent attempt to cook out several corked bottles of Burgundy suggested that some unpleasant flavours remain. Of course I may have wrongly identified the taint as TCA.
I will look into this some more and report back, but will stop short of willing a bottle of corked wine on myself.