In a large nonstick skillet, heat oil until hot but not smoking over medium-high heat. Add the apple, onion, and bacon and cook, stirring frequently, until the apple and onion are softened and the bacon is lightly crisped, about 7 minutes.
Stir in the broth and potatoes and bring to boil. Reduce to a simmer, cover and cook until the potatoes are tender, about 10 minutes.
Meanwhile, in a small bowl, stir together the vinegar, honey, mustard, cornstarch, salt, pepper and 2 tablespoons of water. Stir the vinegar mixture into the skillet, bring to a boil, and cook, stirring constantly, until the mixture is slightly thickened, about 1 minute. Stir in beets and dill weed and cook until the beets ae just warmed through, about 1 minute longer.