Wash mussels very carefully by rinsing several times under running water to remove all impurities. Heat 2 tablespoons of oil in a pan over medium heat, add mussels, cover and cook until they open. Remove from the heat, cool slightly and discard the shells. Set aside in a bowl with one ladleful of strained cooking water.
Reserve remaining cooking water. Wash clams very carefully, rinsing them under running water several times to remove all impurities. Repeat the process of heating 2 tablespoons of oil in a pan and sautéing the clams until they open. Allow to cool, remove the shells, strain cooking water and reserve with the mussels' water. Combine shucked clams with the mussels.
Soften dried mushrooms in warm water for about 20 minutes. Heat 1 tablespoon of oil in a pan over medium heat and sauté mushrooms. Add 2/3 of the reserved seafood cooking water and cook for 4 - 5 minutes.
Add remaining cooking water and the shucked mussels and clams and turn off the heat. Meanwhile, boil pasta in plenty of salted water according to package directions. Drain and toss with the prepared sauce and some chopped parsley.