FAILURE TO NOTE REDUCTION IN ZERO FUEL WT DURING DISTR FLT PREPARATION; FLT CREW OF B737-300 BELIEVE THE ACFT GROSS WT FOR LNDG WILL EXCEED MAX. TAKE MEASURES TO INCREASE FUEL BURN DURING LAST HALF HR OF FLT.

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UPON RECEIVING THE LOAD SHEET AT BDL; I NOTED THAT THE OPS AGENT HAD MADE A CORRECTION TO THE ZERO FUEL WT (CORRECTION FOR CHILD WTS -- 1200 LBS). SHE HAD MADE THE CORRECTION NOT DIRECTLY BELOW THE ORIGINAL ZERO FUEL WT NUMBER; BUT HAD SKIPPED DOWN 2 LINES AND INPUT THE NEW NUMBER. 2 DISTRS OCCURRED DURING THE OPC/FMC INPUT OF LOAD SHEET NUMBERS: 1) A FAMILY OF 4 WAS DENIED BOARDING BECAUSE OF IMPROPER SCREENING. A MISTAKE MADE BY TSA. THEY WERE REMOVED FROM THE BOARDING PROCESS AND TAKEN BACK TO SECURITY FOR RE-SCREENING. UPON RE-BOARDING THE ACFT; THE FAMILY -- ESPECIALLY THE MOTHER -- WAS VERY; VERY UPSET. CUSTOMER SVC AGENT; I; THE CAPT AND THE FLT ATTENDANT WERE ALL INVOLVED IN THE ISSUE WHICH WAS EVENTUALLY RESOLVED BY CUSTOMER SVC AGENT. 2) THERE WAS SENSE OF URGENCY TO PUSH BACK IN ORDER NOT TO LOSE OUR SLOT TIME TO DEST. I INPUT THE ORIGINAL ZERO WT AS OPPOSED TO THE CHILD CORRECTED ZERO FUEL WT INTO THE OPC AND FMC. AFTER AIRBORNE AND APPROX 100 MI FROM DEST; I STARTED FIGURING THE LNDG WT. THE CALCULATION SHOWED US OVER THE MAX LNDG WT. I NOTED THIS TO THE CAPT AND WE CONCLUDED WE NEEDED TO BURN FUEL DOWN IMMEDIATELY IN ORDER TO LAND BELOW OUR MAX LNDG WT. THE CAPT ASKED FOR THE LNDG GEAR DOWN AND THEN FLEW FOR THE NEXT APPROX 25 MINS WITH THE GEAR DOWN AND SPD BRAKES OUT. I MADE A PA TO THE PAX AND FLT ATTENDANTS SO THEY KNEW WHAT WE WERE DOING. LNDG WAS UNEVENTFUL. UPON ARRIVING AT THE GATE. THE CAPT CALLED DISPATCH TO INVESTIGATE THE PROB. THIS IS WHEN HE LEARNED I HAD INPUT THE WRONG ZERO FUEL WT INTO THE OPC AND FMC. THE ERROR OCCURRED MOSTLY DUE TO THE MY INATTN TO DETAIL BUT ALSO BECAUSE OF THE 2 DISTRS; AND BECAUSE THE CORRECTED NUMBER WAS NOT ON THE VERY NEXT LINE BELOW THE ORIGINAL ZERO FUEL WT NUMBER (IT WAS EASY TO MISS IN A RUSH). LESSON LEARNED TO SLOW DOWN WHEN EVERYTHING IS SPEEDING UP AROUND YOU.