Wash the shrimp. Boil water with salt, and as it returns to a boil add the shrimp in their shells and 1 tbsp of the vinegar. Cook 4 minutes (less if shrimp are small), then drain. When cool enough, shell and devein. Set aside.
Trim the green beans and wash. Boil in salted water until tender but still firm, then drain.
Boil the potatoes in their skins in enough water to cover amply until easily pierced with a fork. Drain and peel while still hot.
Peel the carrots and cook them as you cooked the beans, until tender but still firm.
Drop the peas into salted boiling water and cook about 1 minute. Drain and set aside.
Pat the beets dry. After the cooked vegetables cool, reserve a small quantity of each (including beets, but not potatoes) for decoration. Cut the remaining vegetables as directed: green beans into 3/8-inch lengths; potatoes, carrots, and beets into 3/8-inch cubes. Put them in a bowl with the capers and pickles.
Reserve half the shrimp. Dice the rest and add to the bowl. Add the olive oil, remaining 2 tsp vinegar, and salt, then toss. Fold in half the mayonnaise to coat evenly. Taste and correct for salt.
Turn onto a platter (preferably round) and shape into a shallow, flat-topped oval mound. Cover smoothly with the remaining mayonnaise.
Decorate with the reserved vegetables and shrimp as you like.