A B737-300 WING FUEL TANK GAUGE MALFUNCTIONED CAUSING A WING VENT FUEL DUMP. THE PREVIOUS FLIGHT WAS FLOWN WITH AN UNDETECTED OUT OF BALANCE FUEL LOAD BECAUSE OF THE GAUGE MALFUNCTION.

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LANDED 3200 LBS OUT OF BAL IN ZZZ1. THE PROB APPARENTLY STARTED IN ZZZ WHEN THE #1 FUEL QUANTITY INDICATOR FAILED TO PROVIDE THE PROPER DATA. THE FUEL IN READING WAS 7.9. THE REQUIRED FUEL LOAD SHOULD HAVE BEEN FOB BUT WITH THE ERRONEOUS READING 3200 LBS WAS UPLOADED INTO THE ACFT. THE #2 FUEL QUANTITY INDICATING PROPERLY; THE FUELER APPARENTLY PUT ALL 3200 LBS IN THE L SIDE UNTIL THE #1 QUANTITY INDICATOR INDICATED THE REQUIRED READING. THE OPS AGENT HAD A PROB RECONCILING THE FUEL LOAD ON THE LOADSHEET. SHE BROUGHT THIS TO MY ATTN AND DID A FUEL AUDIT. THE AUDIT WAS WITHIN FOM LIMITS; SHOWING A 900 LB DISCREPANCY. I OKAYED THE LOAD AND THE OPS AGENT MADE THE PROPER ADJUSTMENTS ON THE LOADSHEETS. THE FUELER IN ZZZ1 CAME TO INFORM ME HE JUST DUMPED FUEL OUT OF THE L WING VENT; WITH A #1 FUEL QUANTITY INDICATING 5.5. MAINT WAS CALLED AND CONFIRMED THE INDICATOR INOP BY DRIP STICKING THE #1 TANK; WHICH INDICATED FULL. AFTER FUELING THE ACFT THE FUELER PUT IN 17800 LBS INSTEAD OF THE REQUIRED 21000 LB FUEL LOAD; THUS CONFIRMING THE 3200 LB FUEL IMBAL UPON LNDG. SUPPLEMENTAL INFO FROM ACN 813461: WE PUSHED BACK AND HAD AN UNEVENTFUL FLT TO ZZZ1; IT WAS THE CAPT'S LEG. ON THE GND IN ZZZ1 I WAS STANDING AT THE ENTRY DOOR TO THE COCKPIT AND HEARD SOMEONE YELLING; 'SHUT IT OFF!' I LATER LEARNED THAT THIS WAS GND PERSONNEL YELLING BECAUSE THE FUEL WAS VENTING OUT OF THE #1 TANK WHILE THEY WERE FUELING FOR THE SUBSEQUENT LEG. AT THAT TIME; THE #1 GAUGE WAS READING ABOUT 5.5 AND A SUBSEQUENT DIPSTICK REVEALED THAT THE TANK WAS FULL. THE GAUGE WAS MEL'ED AND FUEL VERIFIED; AND WE CONTINUED UNEVENTFULLY. AFTER LOOKING OVER THE DATA (LOADSHEETS; RELEASES; ETC); THE CAPT FEELS THAT THERE WAS AN UNBALANCED FUEL LOAD OF GREATER THAN 1000 LBS WHEN WE LANDED. I FEEL THAT THIS IS POSSIBLE; BUT (FOR REASONS STATED ABOVE) I AM REALLY NOT SURE HOW MUCH OF A SPLIT THERE WAS. AS FOR A SUMMARY OF THREATS AND ERRORS; WE OBVIOUSLY HAD A FUEL GAUGE MALFUNCTION AND BOTH THE CAPT AND I FAILED TO NOTICE THIS. I WILL SAY THAT THE GAUGE SEEMED TO READ MORE ACCURATELY WHEN IT WAS BELOW 5.5 LBS; AND THE FUEL REQUIRED FOR FLT WAS SO CLOSE TO THIS 5.5 (IN THAT TANK) LOAD; THAT WE DID NOT NOTICE THE INCONSISTENCY UNTIL A GREATER FUEL LOAD (FOR OUR NEXT LEG) WAS REQUIRED. AN INCONSISTENCY IN THE LOAD WAS DETECTED BY THE GATE AGENT; BUT APPARENTLY AN ERROR WAS MADE IN THE FUEL AUDIT AND WE ADDED FUEL AND WENT AWAY.