well just using it sparingly on the meat is a good start...a simple au jus or thicken it up with a bit of flour and milk and have a good gravy for the potatoes or even vege. Or if making a soup soon, store the liquids and remove the fat cap the next day and use it as a sort of stock. I have also had a Chef just toss it in a store BBQ sauce to give it a bit more flavor and loosen it up.
It makes a good cooking liquid for rice. Once the rice is cooked, I add frozen vegies and leftover pork. Then, I taste it and add what ever flavors are missing. (that, or I taste it first... then also last..)
I thought he just added a bottle of ginger ale to his braising liquid. Depending on the brand (I think the deep ginger flavor of a Reed's ginger ale would be a good one) it could add a mild sweet ginger flavor to the meat. I think after all the slow cooking the left over liquids should make a fine tasting gravy too.
Use the braising liquid from a pork butt or shoulder to make your masa dough for tamales. Then use the pork itself for the filling.
Add it to anything you make that requires liquid, sauces, soups, rice, beans, or grains. Savory grits or polenta come to mind. Quinoa would work too. Pork stock with a little vinegar makes slow cooked greens authentic.