B737 FLT CREW FAILS TO DETECT MEL MISSING FROM RELEASE PRIOR TO DEPARTURE.

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ORIGINATING ACFT HAD 3 MEL'S. ONE WAS A CREW DEFERRAL FOR AFT GALLEY WATER PRESSURE INOP. ONE OF THE OTHERS WAS A FUEL GAUGE MALFUNCTION; WITH A RELATED MEL LISTED ON THE RELEASE. THIS MEL REQUIRED THAT I OBSERVE A DRIP STICK MEASUREMENT OF FUEL QUANTITY. IN ADDITION TO ACFT PREFLT AND PREPARATION DUTIES; I BRIEFED THE FLT ATTENDANTS ON THE GALLEY WATER PRESSURE PROB AND THE INFLT WX (SIGNIFICANT) FOR THE LEGS WE'D FLY TOGETHER. THE FO AND I CAREFULLY READ THE MEL PERTAINING TO THE INOP FUEL GAUGE; TO INCLUDE THE REQUIREMENTS TO TRACK FUEL USED AND UPDATE THE FMC PRIOR TO DEP. DUE TO THE COMPRESSED TIMELINE INVOLVED; I FAILED TO AUDIT THE NUMEROUS MEL AND MAINT NOTE STICKERS AND DID NOT NOTICE THE CREW DEFERRED GALLEY WATER PRESSURE HAD NOT BEEN ADDED TO THE RELEASE. I NOTICED THIS ONCE AIRBORNE. THE WATER PRESSURE PROB WAS CORRECTED IN ZZZ AND THE MEL REMOVED. WITH 3 MEL'S LISTED ON THE RELEASE AND 3 MEL STICKERS IN THE LOGBOOK; I ASSUMED THE ONES LISTED ON THE RELEASE WERE THE PROPER ONES. IN REALITY; THE 'EXTRA' MEL WAS FOR THE FUEL SUMMATION UNIT; AN ASSOCIATED MEL FOR THE INOP FUEL GAUGE MEL. IN MY HASTE TO COMPLY WITH DRIP STICK MEASUREMENT REQUIREMENTS; UNDERSTAND THE FUEL QUANTITY MONITORING PROCESS; BRIEF MY FO; AND GET THE ORIGINATOR READY TO GO I DID NOT PROPERLY AUDIT THE MEL'S SHOWN ON THE RELEASE AGAINST THOSE IN THE LOGBOOK. I JUST COUNTED THE MEL'S (3 ON THE RELEASE AND 3 IN THE LOGBOOK). I'VE ALWAYS DONE A COMPLETE AUDIT IN THE PAST; AND HAVE CAUGHT ERRORS IN THE RECORDS OR THE RELEASE. I GOT A BIT COMPLACENT AND IN A HURRY TO GET THE JOB DONE. WHAT NEEDS TO HAPPEN IS TO DELEGATE THE TASK OF DOING THIS REVIEW TO THE OTHER PLT; AND/OR DO A THOROUGH REVIEW MYSELF AND TAKE A LATE DEP; IF NECESSARY. THIS WAS A FAIRLY MINOR ITEM; AGAINST THE CHALLENGES WE FACED THIS MORNING; BUT STILL A 'GOTCHA' I SHOULD HAVE CAUGHT. SLOW DOWN; MAKE SURE THE PAPERWORK MATCHES REALITY; AND ASSUME NOTHING.