A B747-400 FLT CREW AND DISPATCHER RPTED THAT THE ACFT DEPARTED SFO WITH THE WRONG FMC DEFERRED INOP.

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ACFT HAD NUMEROUS FMC PROBS BOTH L AND R FMC'S HAD BEEN ALTERNATELY INOP. THE MRD WAS VERY LONG AND COMPLEX AND DUE TO VARIOUS ITEMS DURING PREFLT HAD BEEN SENT MORE THAN ONCE. WE WERE DISPATCHED WITH FMC LEFT INOP. THIS IS WHAT LOGBOOK AND PAPERS SAID. AS IT TURNED OUT; THE L FMC WAS OPERATIVE AND THE R FMC INOP. THE R FMC WAS DEFERRED XXA AND THE L FMC WAS DEFERRED XXB. THIS ERROR WAS NOT CAUGHT ON A VERY BUSY PREFLT. THE L FMC APPEARED TO OPERATE NORMALLY. RECEIVED AN ACARS FROM ACR ABOUT IT. WE REALIZED THE ERROR. WE IMMEDIATELY NOTIFIED DISPATCH AND ALSO BEGAN TO UTILIZE RAW DATA NAV TO INSURE THAT OUR FLT WAS ACCURATELY NAVED AND FLOWN. MAINT APPARENTLY FIXED THE L FMC BUT DOCUMENTED IT AS THE R FMC. I FAILED TO CATCH THE ERROR AND THE ACFT WAS FLOWN. THE MAINT RELEASE WAS VALIDATED BEFORE DEP AS TO NUMBER AND TIME. THE MEL CARD WAS PRESENT IN THE LOGBOOK. SUPPLEMENTAL INFO FROM ACN 588432: DURING PREFLT WE HAD A DEFERRED L FMC ON OUR FLT PAPERS. WE GOT TO THE ACFT AND I STARTED TO SET UP THE ACARS AND NOTICED THERE WAS A DEFERRAL STICKER ON THE MASTER FMC AND THE FO FMC SECTOR SWITCH. WE GOT A MESSAGE FROM LINE MAINT THAT A NEW MAINT RELEASE WAS ON ITS WAY TO THE PRINTER. I RETURNED TO THE COCKPIT. THE CAPT TOLD ME HE REVIEWED THE NEW MAINT RELEASE AND STATED THAT THE FO FMC SELECTOR HAD TO BE SELECTED TO THE L FMC POS; THAT THE NEW DEFERRAL ITEM WAS AN INOP R FMC. WE ALSO HAD A STATUS MESSAGE 'FMC R'. IN CRUISE; MAINT TOLD US THE LINE MAINT DID NOT UPDATE THE MAINT RELEASE WITH THE R FMC INOP AND CAPT MISREAD THE NEW MAINT RELEASE. IN THE FOM THE CAPT HAS THE RESPONSIBILITY TO REVIEW THE LOG BUT IT SHOULD BE REVIEWED AS A TEAM. I MIGHT HAVE CAUGHT THE MISTAKE INSTEAD OF GETTING A BRIEFING FROM THE CAPT. SUPPLEMENTAL INFO FROM ACN 588429: WAS INFORMED ENRTE BY THE CAPT THAT THE L FMC; MEL XXA WHICH WAS SHOWING DEFERRED AND RELEASED AS SUCH FOR THIS FLT; WAS OPERATING NORMALLY. I WAS FURTHER ADVISED THAT THE R FMC WAS INOP. MAINT CONCURRED VIA TELEPHONE THAT THE ACFT WAS IN FACT IN THIS CONDITION; AND THAT THE ITEM WOULD BE REVIEWED UPON ORD ARR FOR PROPER REDEFERRAL USING MEL REF XXB. THE FLT CONTINUED SAFELY TO ORD. ROUTINE ARR FOR EXPECTED MAINT INSPECTION.