Add cubed red potatoes to a Dutch oven of water and bring to a boil over high heat, then reduce to a steady simmer until tender, 15 to 20 minutes. Visual cue: a fork should slide in easily with no resistance.

Drain the potatoes in a colander and let them cool completely, 15 to 25 minutes. Visual cue: the cubes look matte and warmness is gone.

In a large bowl, combine the cooled potatoes, chopped dill pickles, diced celery, and finely diced red onion. Visual cue: pickle chunks are evenly dotted through the potatoes.

In a separate bowl, whisk together mayonnaise, dill pickle juice, Dijon mustard, salt, and pepper until smooth and creamy, 1 to 2 minutes. Visual cue: the dressing thickly coats the whisk with an even pale color.

Pour the dressing over the potato mixture and toss well until every piece is coated, 1 to 2 minutes. Visual cue: the potatoes look glossy and uniformly speckled.

Fold in the chopped fresh dill gently so it stays bright and evenly distributed. Visual cue: green flecks appear throughout without being mashed.

Refrigerate the salad for 2 hours before serving to let flavors meld, 2 hours. Visual cue: the salad firms up slightly and looks creamy-chilled at the edges.