What was found
PILOT REPORTED 'GEAR UNLOCKED' LIGHT STAYED ON WHEN GEAR SELECTED UP AFTER TAKEOFF. AFTER A FLY-BY, THE TOWER TOLD PILOT NOSE GEAR WAS HANGING DOWN, IN TRAIL. PILOT SELECTED GEAR DOWN AND ALL 3 GREEN DOWN AND LOCKED LIGHTS CAME ON AS THE UNLOCKED LIGHT WENT OUT. A NORMAL LANDING WAS MADE AND ACFT WAS TURNED OVER FOR REPAIR. INSPECTED THE LANDING GEAR RETRACTION SYSTEM AND FOUND BOTH NOSE LANDING GEAR RETRACT ACTUATOR ATTACH LUGS (PN 5713040-22'S) HAD BROKEN WHERE THEY ATTACH TO THE END BOSS OF THE ACTUATOR. THIS PROBABLY HAPPENED WHEN THE GEAR WAS SELECTED UP AFTER TAKEOFF AND ALLOWED THE NOSE GEAR TO TRAIL IN THE SLIPSTREAM.