Cover potatoes with salted water by 1 inch in a large saucepan, then simmer, uncovered, until just tender, about 15 minutes.
Drain in a colander and rinse under cold water until cool.
Prepare grill for cooking.
Cut cooled potatoes crosswise into thirds and arrange in 1 layer on a tray.
Brush both sides of potatoes with some oil (2 tablespoons total for all of them) and season with salt and pepper.
When fire is medium-hot (you can hold your hand 5 inches above rack 3 to 4 seconds), grill potatoes on lightly oiled rack until grill marks form, about 1 minute on each side, then transfer to a large bowl. Toss hot potatoes with 2 tablespoons lemon juice.
Put mussels in aluminum pan and cook in covered grill, stirring occasionally, 5 to 6 minutes, or until they just open.
Transfer mussels to a bowl with a slotted spoon. Discard any that haven't opened, then shuck remainder.
Add mussels to potatoes along with fennel, parsley, olives, capers, and remaining 2 tablespoons lemon juice, tossing to combine, then let stand at room temperature, tossing occasionally, 10 minutes.
Toss salad with remaining oil and salt and pepper to taste.
