Chilled glasses: You'll notice some bartenders will fill your glass with ice water and drain it off before pouring the cocktail in. (An even better method is ten minutes in the freezer.)
Cold, cracked ice: If you've ever been served a warm or diluted cocktail you can blame the ice (and an indifferent bartender). Cracked or chipped ice has more surface area to chill a cocktail efficiently. Reusing ice is also a fruitless path to potency. A high caliber drink will have tiny slivers of ice floating on the top.
Fresh citrus juice: The next time you order a premium margarita, take a look at how it is made. Sour mix from the bartender's gun is equivalent to liquid Jolly Ranchers. The oil from the skins of fresh-squeezed or muddled citrus will add levels of depth and flavor to a cocktail.
Classic mixers: An apple martini can easily be made with vodka and sour apple liqueur, but far superior is a classic Jack Rose made with applejack brandy, fresh lime juice and grenadine. Any cocktail bar worth its salt will have fixings like applejack, real Maraschino, Chartreuse and absinthe, among others, to flesh out its concoctions.
Brand independence: A cocktail menu dominated by brands generally indicates that the menu was mainly constructed by salespeople, not serious bartenders. Lack of effort on a menu can equate to lack of effort at the mixing stage. Look for a menu that emphasizes balanced combinations over brands.
Accoutrements: Your bartender ought to know that swapping pickled onions for the olives in a martini turns the drink into a Gibson, and will stock the garnish to accomplish such a noble mission. Bottles of bitters and flower waters must be handy. As should citrus curls and mint leaves. Find a joint that knows to toss an egg white into the shaker when you order a Pisco sour and you might as well stay for a few.
