Place the potatoes in a large pot and add enough cold water to cover by 2 inches. Add 1 tablespoon of the salt and bring to a boil. Reduce heat to medium-low. Simmer until the potatoes are fork-tender, about 15 minutes. Drain and set aside. Meanwhile, in a skillet, over medium heat, fry the bacon until crisp, about 7 minutes, then transfer it to a paper towel–lined plate. In a small bowl, whisk together the mustard, vinegar, pepper, and the remaining 1 teaspoon of salt. Whisking constantly, slowly add the oil in a steady stream until an emulsion forms. Cut the potatoes into bite-size pieces and place in a bowl. Add the bacon, corn, and vinaigrette and toss. Serve at room temperature.