Put potatoes in a large pot with enough salted water to cover by 2 inches, and bring to a boil. Cook 25 to 35 minutes, or until potatoes are just tender when tested with a knife. Drain and peel when potatoes are cool enough to handle, then dice.
In a large bowl, toss together potatoes, bacon, onion, and celery. In a jar with a tight-fitting lid, combine vegetable oil, vinegar, mustard, salt, and pepper. Shake well to blend, then pour over potato mixture and toss to coat.