WHEN THE WING FLAPS WERE RETRACTED AFTER TAKEOFF, THE CAPTAIN NOTED AIRFRAME VIBRATION. HE DUMPED FUEL AND RETURNED TO LAND. EXAMINATION OF THE AIRPLANE REVEALED THAT THE NO 1 MOVABLE FLAP FAIRING WAS MISSING. THE FAIRING WAS LOCATED THE NEXT DAY IN A FIELD APPROXIMATELY 3 MILES FROM THE TAKEOFF RUNWAY. EXAMINATION OF THE FAIRING REVEALED THAT THE TWO, LOWER HINGE BOLTS WERE MISSING. THE HINGES AND BUSHINGS SHOWED NO EVIDENCE OF DEFORMATION OR FAILURE.