DURING GEAR RETRACTION AFTER TAKEOFF, THE AIRCREW NOTED THAT THE LEFT MAIN LANDING GEAR (MLG) DOOR WARNING LIGHT REMAINED ILLUMINATED. THE LANDING GEAR CONTROL WAS CYCLED, BUT THE CONDITION WAS NOT CORRECTED. ATTEMPTS TO EXTEND THE LEFT MLG WERE ALSO UNSUCCESSFUL. DURING TOWER FLY-BY'S, THE AIRCREW WERE ADVISED THAT THE NOSE & RIGHT MLG WERE DOWN; HOWEVER, THE LEFT MLG WAS ONLY PARTIALLY EXTENDED & THE LEFT MLG DOOR WAS IN AN APRX 45 DEG POSITION. SUBSEQUENTLYA WHEELS UP LANDING WAS MADE. AFTER BEING HOISTED, THE LEFT MLG WAS FOUND HANGING DOWN & WEDGED ON THE DOOR. ALL GEAR WERE EXTENDED & THE ACFT WAS TOWED FROM THE RWY. AN EXAM REVEALED NO DISCREPANCIES EXCEPT THE LEFT MGL DOOR ACTUATOR MOUNTING BOLTS & A SERRATED FITTING WERE LOOSE. THE SYSTEM MALFUNCTION COULD NOT BE DUPLICATED. THE ACFT WAS EQUIPPED WITH AN ORIGINAL PRODUCTION MLG SAFETY BAR TO PREVENT INTERFERENCE BETWEEN THE DOOR & GEAR DURING EMERGENCY EXTENSION WITHOUT HYD PRESSURE. HOWEVER, IT WAS NOT DESIGNED TO WITHSTAND DOOR CLOSING PRESSURES (HYD & AIR).