Seeing exhaust residue on any vehicle doesn't seem right at all. It sounds like something is clogging up somewhere in emissions system, or maybe you have dirty fuel injectors.
Try inserting some fuel injector cleaner fluid into the fuel tank. Any brand will do, but most people opt for Chevron w/ Techron concentrate; they're one of the best in the market. It's about $6 per bottle to treat up to a 12 gal in a fuel tank, and you can purchase it at any auto parts store like Autozone and Pep Boys. After putting fuel injector cleaner, wait until 2 fill-ups afterwards and see if there's any difference.