Over high heat, bring a large pot of water to boil. Meanwhile, cut potatoes in half lengthwise, then crosswise into 1/4-inch slices. Add potato slices to boiling water; return to boiling and simmer 5 - 6 minutes or until tender, but firm. Drain potatoes and set aside or refrigerate.
In a large bowl, combine dressing and ginger; toss dressing with dill and chopped vegetables. Gently stir in potatoes and smoked salmon.
To serve, arrange lettuce leaves on a platter (or on individual dishes), top with salad mixture.