While the potatoes are boiling, you'll maximize your time efficiently. Finely dice the pickles into 1/4-inch pieces, mince the shallot, and freshly chop the dill (I find fresh dill makes a huge difference in aroma and flavor compared to dried). Measure out the capers and set aside. Start boiling the potatoes in salted water—I use Yukon Gold potatoes because they maintain a creamy texture and don't fall apart during cooking. Cut them into roughly equal-sized pieces so they cook evenly, then boil for about 25 minutes until fork-tender.
While the potatoes finish cooking, combine the mayonnaise, olive oil, caper liquid, mustard, and garlic powder in a small bowl. Whisk these together until smooth and well-blended. I prefer Hellmann's mayonnaise for this salad because it has a clean taste that won't overpower the dill, and Grey Poupon mustard adds a nice sharp kick without being too intense. Have this ready to dress the potatoes while they're still warm, which helps the flavors absorb better.
Once the potatoes are tender, drain them in a colander and rinse with cold water briefly to stop the cooking process. This prevents them from becoming mushy. Transfer the cooled potatoes to a large mixing bowl and immediately pour the dressing from Step 2 over them while they're still warm. The warmth helps the potatoes absorb the flavors more effectively. Stir gently to coat all the potato pieces evenly with the dressing.
Add the minced shallot, diced pickles, chopped dill, and capers from Step 1 to the dressed potatoes. Mix everything together gently but thoroughly, making sure the vegetables and herbs are distributed evenly throughout. Taste the salad and season with salt and freshly ground black pepper to your preference—start with a light hand since the pickles and capers already contribute salty, briny flavors. Serve immediately or chill until ready to serve.