OPEN LOGBOOK WRITE-UP NOT DISCOVERED BY FLC UNTIL AT CRUISE.

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ENRTE; I WENT TO FILL OUT OUR LOGBOOK AND DISCOVERED AN OPEN LOGBOOK WRITE-UP. THE PREVIOUS CABIN CREW HAD USED A PORTABLE OXYGEN BOTTLE AND IT HAD BEEN WRITTEN UP TO BE REPLACED. I DON'T KNOW IF THE COCKPIT CREW HAD NOTIFIED MAINT BY RADIO; AND THEY NEVER GOT TO THE PLANE BEFORE WE PUSHED; OR IF IT HAD BEEN WRITTEN UP WITH NO NOTIFICATION. I HAD ACTUALLY CHKED THE COVER OF OUR LOGBOOK AGAINST OUR RELEASE TO VERIFY THAT THE MEL ITEM ON THE ACFT MATCHED THAT ON OUR PAPER WORK. BUT I DID NOT OPEN THE LOGBOOK TO CHK FOR ANY NEW DISCREPANCIES. I HAD SEEN BOTH OF THE PREVIOUS CREW MEMBERS LEAVING THE PLANE BUT NEITHER MENTIONED THE WRITE-UP; NOR WERE THEY REQUIRED TO. I ALWAYS TRY TO GIVE AN ONCOMING CREW A HEADS UP ABOUT ANYTHING WE WROTE UP SO THEY CAN MAKE SURE TO HAVE THEM CORRECTED BEFORE THEY GO; AND DON'T WIND UP LIKE WE DID THIS FLT. THERE HAD BEEN A LOT OF NONSTANDARD ACTIVITY IN THE FORWARD GALLEY AND JETWAY PRIOR TO OUR DEP; BUT IT CAME DOWN TO THE FACT THAT NEITHER THE CAPT NOR I TOOK 2 SECONDS TO OPEN THE LOGBOOK AND CHK IT. I HAD FLOWN WITH THIS CAPT THE PREVIOUS WK AND DURING BOTH TRIPS HE ALWAYS SIGNED THE LOGBOOK BEFORE WE LEFT THE GATE; BUT NOT THIS TIME. OUR CHKLIST SAYS 'LOGBOOK -- ON BOARD.' BUT I'M NOW USING THAT AS MY CUE TO MAKE SURE IT HAS BEEN CHKED AND ANY OPEN ITEMS CLRED.