Trim the ribs and cut the rack into 4 sections. Rub the ribs generously with your favorite rib rub. If you don't have a rib rub, salt, pepper, and garlic powder will work just fine. Allowing the ribs to sit in the refrigerator a while (even overnight) will add more flavor, but it isn't required.
Mix the vinegar, soy sauce, and liquid smoke together and pour it into the bottom of the slow cooker. Add the rib sections, spreading them around the bowl of the slow cooker. Cook on low for 4 to 6 hours, or until tender and you can see the meat separating from the bone.
Preheat the grill to medium-high heat. Coat the ribs with the barbecue sauce and grill for 15 minutes, turning once, or until the barbecue sauce is charred a bit.