You see, smell, or taste liquid smoke
Liquid smoke is made from torching wood chips and funneling the smoke into a condenser, where it cools and drips while more water is added to bulk up the smoky brew (think redneck molecular gastronomy). It has a highly concentrated smoky flavor, and when dumped into marinades, sauces, or mops, liquid smoke produces an unholy and unmistakable chemical note. Any restaurant which uses smoke flavor poured from a bottle is covering up the fact that their "barbecue" is cooked in a gas or electric oven. The waft of a line cook's Camel unfiltered is the closest your meat ever got to smoke.
They proudly advertise ribs that "fall off the bone"
If eating the barbecue doesn't require your central and lateral incisors (and the meat could be sucked, with just a little effort, through a straw), the restaurant is boiling and/or steaming the meat first and grilling or broiling it to finish, which gives brisket, ribs, and pulled pork the appearance of being cooked over flames. Properly cooked ribs may pull or tear clean off the bone, but they should never slide off. Amateurs might call it tender, but barbecue traditionalists know a fake by the telltale mushy, flavorless, and overcooked meat Jell-O they serve.