Bring a large pot of lightly salted water to a boil. Cook potatoes in boiling water until tender yet firm, about 15 minutes. Drain and place in a large serving bowl.

Place eggs in a saucepan and cover with cold water. Bring to a boil, then immediately remove from heat. Cover the pan and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water and allow to cool. Peel and chop eggs. Add to potatoes in the serving bowl. Stir in mixed vegetables until combined.

Make dressing: Combine mayonnaise, olives, lemon juice, pepper, mustard, dill, and salt in a separate bowl; stir until blended.

Pour dressing over potato mixture. Season with salt and pepper; toss to coat. Cover and refrigerate until chilled, at least 1 hour to overnight.