1. Scrub potatoes.
2. In a 3- to 4-quart covered pan over high heat, bring 1 1/2 quarts water to a boil. Add potatoes, cover, and simmer until they are just tender when pierced in thickest part, 20 to 30 minutes.
3. Drain potatoes and cover generously with cold water. Drain when cool, about 15 minutes.
4. Meanwhile, mix vinegar, oil, parsley, and mustard in a wide bowl.
5. Peel potatoes. Cut potatoes and beets into 1/2- to 3/4-inch cubes and add to bowl. Add onion, mix gently, and season to taste with salt and pepper.