Place potatoes in a large saucepot filled with 2 quarts water seasoned generously with salt. Bring water to simmer and cook for 10–15 minutes, or until a fork can be easily inserted into the potatoes.
Drain potatoes and place on baking sheet. Let cool in the refrigerator.
Meanwhile, whisk mustard and vinegar together. While whisking, slowly drizzle in olive oil until dressing has emulsified and is well-blended. Mix in lemon juice. Season to taste with salt and pepper.
Place cooled potatoes in a large bowl with celery, red onions, chives, parsley and dill.
Toss salad with dressing. Season to taste with salt and pepper.