Fishing for praise
How invested in your experience is the bartender? Is he as interested in your enjoyment of the time you're spending at the bar as he is in how you're enjoying his creation? I find that the more a bartender needs to be told how great his drink is (whether it is or not), the less likely he's good at the actual, overarching job of bartending. If your man behind the stick is happy to serve you and be unobtrusive while doing so, you're finally starting to win.
Lopsided menu offerings Unless it's part of the ethos of the bar in question, the menu should offer a varied range of styles and flavors. If it's all martinis, they aren't trying to reach a broad audience. Likely because they aren't filled enough to do so.
Watch their reaction to your reaction So, you made a leap of faith and chose a drink you thought sounded delicious. But then it turns out that, although it was made the way it should've been, it simply doesn't suit your taste. If the barman makes you feel inferior or even stupid rather than removing the drink and offering you something else, it's time to leave. It should never be a problem to make you something you'll enjoy.
Keep an eye on price vs. value This sword cuts both ways. Was the drink perfect, yet served in a plastic cup by a muscle shirt-clad bartender and only cost $5? Hey, if it's amazing, don't balk! Or, was the $23 beverage mediocre, but served at a beautiful rooftop bar? That place is fooling you! When the price doesn't reflect the value, the emphasis is less on the drinks and more on volume or revenue.