A faulty wine and a wine you dislike are different things, and the distinction matters because one is a returnable defect and the other is not. The good news is that the common faults are specific and learnable. Once you have smelled cork taint knowingly, you will never mistake it again.
Cork taint
The compound is TCA, 2,4,6-trichloroanisole, and it forms when chlorine compounds meet mould in cork bark or in a winery's woodwork. It smells of wet cardboard, damp cellar, wet dog or a mouldy newspaper, and it is detectable by many people at a few parts per trillion, which is among the lowest thresholds for any smell humans perceive.
It does not always announce itself. At low concentration it does not smell mouldy at all; it simply removes the fruit, and the wine tastes muted, short and dull for no obvious reason. That is the more common and more frustrating version.
It is a fault, it is nobody's fault in particular, and any restaurant or shop will replace the bottle. Historically it affected a few percent of cork-sealed bottles. It cannot occur under screwcap, which is the main reason Australia and New Zealand moved away from cork.
Oxidation
Too much air. The wine turns brown at the rim, loses its fresh fruit and smells of bruised apple, sherry, nuts or caramel. In a young white it is a fault. In an old wine it is the natural end of a long life, and telling the two apart is a matter of what the wine was supposed to be.
Some styles are oxidised deliberately and are not faulty at all: sherry, tawny port, Madeira and vin jaune are made this way on purpose, and they will smell nutty and appley by design.
Reduction
The opposite problem: not enough oxygen during winemaking, producing sulphur compounds that smell of struck match, burnt rubber, boiled cabbage or, at worst, drains. Mild reduction is fashionable in some circles and often blows off after fifteen minutes in the glass or a vigorous decant. Severe reduction does not, and that is a fault.
If a wine smells odd on opening, pour a glass and wait ten minutes before judging it. Reduction improves with air; cork taint does not.
Heat damage
A bottle left in a hot car, a sunlit shop window or an uninsulated warehouse cooks. The wine tastes stewed and flat, the fruit turns to prune, and the cork may be pushed slightly proud of the bottle or show seepage down the side. Check the top of the capsule before opening a bottle that has had an uncertain journey.
Things that are not faults
Crystals in the bottom of the bottle or on the underside of the cork are tartrates, sometimes called wine diamonds. They are harmless potassium bitartrate, precipitated by cold, and if anything they suggest the wine was not aggressively filtered.
Sediment in an old red is normal and expected; stand the bottle up for a day and decant off it.
A slight fizz in a young white is sometimes deliberate, to keep the wine fresh. In a red it usually means an unintended refermentation, which is a fault.
Brettanomyces, a yeast that gives farmyard, plaster and band-aid notes, is genuinely contested. A little adds complexity to some traditional reds; a lot is a fault. Where the line falls is a matter of taste, and the trade argues about it.