A B737 FLT CREW DEPARTED WITH AN MEL THAT WAS NOT LISTED ON THE RELEASE.

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ACFT ARRIVED AT GATE WITH WRITE-UP. THE WRITE-UP WAS FOR INOP ACARS. MAINT DEFERRED ACARS. ALL LOGBOOK PAPERWORK COMPLETED CORRECTLY. THE CAPT ARRIVED TO THE ACFT LATE. I INFORMED HIM OF THE WRITE-UP AND HE ACKNOWLEDGED. WE PERFORMED NECESSARY CHKLISTS AND LEFT. PUSHBACK; TAXI; TKOF; AND CLBOUT WERE ROUTINE. AT THE TOP OF CLB; THE CAPT NOTICED THE MEL HAD NOT BEEN ADDED TO THE RELEASE. THE CAPT CALLED OPS TO GET A PEN AND INK CHANGE FOR AN AMENDED RELEASE. OPS SAID SINCE WE WERE AIRBORNE; THEY COULD NOT DO THAT. WE ADDED THE MEL TO THE RELEASE WITH THE APPROPRIATE INFO THAT WE HAD. ONCE ARRIVING AT OUR DEST; WE CALLED MAINT TO MAKE SURE THE DEFERRAL WAS IN THE COMPUTER. THERE WAS A COM FAILURE ON THE PART OF SEVERAL PEOPLE; INCLUDING THE FLT CREW; THAT ALLOWED THE FLT TO DEPART WITH INCOMPLETE PAPERWORK. A DIFFERENT SYS THAT ELIMINATES LONG LINES OF COM AND THAT CAN HANDLE DEFERRED ITEMS IN A MORE TIMELY MANNER NEEDS TO BE DEVELOPED. FURTHERMORE; CREW COM COULD HAVE MORE COMPLETELY ADDRESSED THE PROB HAD WE HAD TIME TO DISCUSS IT AS PART OF OUR PREFLT BRIEF.