A well-tuned exhaust system has a number of benefits, with one being better fuel economy. So, pay attention to how often you head over to the pump. More trips than usual could mean your vehicle has a problem. Another helpful way to tell is if you have a newer model that tracks fuel economy on the dash. This will help you monitor month-over-month performance and catch a problem before it becomes serious.
Last but not least, the most obvious sign is a drastic change in the volume of your muffler. When working properly, the muffler should operate quietly in the background. When something goes wrong, it becomes a roaring monster. These loud noises are often telltale signs that you should have your exhaust system checked out by a mechanic.