Place the diced potatoes into a large pot. Pour vinegar and water over potatoes. Bring to a boil, reduce heat to a simmer, cook until potatoes are fork tender, about 15-20 minutes. Drain potatoes and allow to cool for about 15 minutes.
In a small bowl, whisk together mayonnaise, mustard, dill, salt, and pepper until well combined.
Place cooled potatoes into a large bowl with radishes and red onion. Pour dressing over all. Gently toss to combine. Potato salad can be served immediately or chilled until ready to serve.