Scrub and clean the potatoes. Cut them into bite-sized cubes.
In a pot, boil the potato cubes in salted water until fork-tender but still firm (15-20 minutes).
In a mixing bowl, combine mayonnaise, Dijon mustard, chopped dill, salt, pepper, and white wine vinegar if using. Mix well.
Once the potatoes are cooked and slightly cooled, gently fold them into the dressing.
Add chopped celery and red onion to the bowl, ensuring even distribution.
Refrigerate the potato salad for at least 1 hour to allow the flavors to meld and the salad to cool.
Before serving, give the potato salad a final gentle toss to ensure the dressing coats all the ingredients.
Garnish with additional dill if desired.
Serve the dill potato salad as a refreshing side dish at picnics, barbecues, or family gatherings.