I'd say the quality with the faded/blended inks, the detail, and the anatomy/proportions. The look and presentation of the shop itself speaks volumes about the artists in the shop. You won't find a great tattoo artist in a dingy, dirty shop. Remember, this is technically a minor medical procedure, so run from a dimly lit, cramped, and dingy shop.
But the No. 1 rule of thumb is to look at an artist's work—all of it! Look at the lines closely. Do they look nice and thin and clean and crisp? Do they look like they have bled, like holding a marker on paper too long? Does the skin look beat-up and red and bleeding? Look at the detail in the pieces in the artist's portfolio. Minute details are the difference between someone who wants to get you in and out of the seat for money and someone whose focus is solely making a great tattoo. Look for saturation and boldness of colors. Packing solid color into skin is difficult if inexperienced, and most will beat up the skin, and you will see blood and areas of light color.