Put hazelnuts in an 8- or 9-inch pan. Bake in a 350° oven until golden beneath skins, 12 to 15 minutes. Pour onto a towel; let cool. Rub nuts in towel to remove loose skins. Lift nuts from towel and reserve; discard skins.
Grate 1/2 teaspoon peel from 1 tangerine. Cut tangerine in half and ream 1/4 cup juice; use another tangerine if necessary. Put peel and juice in a wide, shallow bowl. Peel remaining tangerines. Pull each apart into halves. Cut halves crosswise into 1/4-inch-thick slices. Add to bowl. Pit dates and quarter lengthwise. Add dates, lemon juice, and olive oil to bowl.
Add lettuce and radicchio to bowl, mix, and add salt and pepper to taste. Sprinkle with hazelnuts.