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Cut the potatoes in half if they are large, put them in a pot and add enough lightly salted water to cover them by 2 inches.
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Bring to a boil, and boil gently, uncovered, for about 15 minutes, until just tender. Drain.
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While the potatoes are still warm, peel and slice, or cube them, into a large serving bowl.
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In a skillet, cook the bacon until crisp. Drain. Pour out all but 2 tablespoons of bacon fat. Add scallions and celery, and cook until soft, about 2 minutes. Mix with potato pieces.
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In the same skillet, mix 1/4 cup of water with cider vinegar, sugar, salt, paprika and dry mustard.
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Stirring with a whisk, bring to a boil and pour over salad. Crumble bacon over the top, and serve warm.
