During the pre-flight inspection, the pilot of the Cessna 402 noticed an unusual amount of free play in the elevator trim tab system. A maintenance inspection did not detect any abnormality. During the subsequent flight, while in the cruise, the aircraft suddenly pitched nose down without any input from the pilot. He disconnected the autopilot but this did not remedy the pitch problem. Re-trimming the aircraft also made no difference to the pitch down tendency. After an uneventful landing at the destination, an inspection by a licenced aircraft maintenance engineer revealed that the bolt attaching the trim tab actuator rod to the trim jack could not be located.