MD80 FLT CREW REPORTS ROLLING FORWARD AFTER PUSH BACK DUE TO POSSIBLE PARKING BRAKE FAILURE.

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DURING PUSHBACK THE CAPT INCORRECTLY SET THE PARKING BRAKE WHILE THE TOW BAR AND TUG WERE BEING DISCONNECTED. AFTER #1 ENG WAS STARTED; THE CAPT XMITTED TO THE TUG DRIVER; 'NORMAL START; PARKING BRAKES SET; CLRED TO DISCONNECT.' AS THE TUG PULLED FORWARD AND CLR; THE ACFT ROLLED FORWARD. ALL THE GND CREW SAFELY CLRED THE AREA. THE FLT CONTINUED UNEVENTFULLY. PRIOR TO GATE DEP; THE L BRAKE PRESSURE BLEED DOWN WAS OUT OF LIMITS; REQUIRING THE CAPT TO PUMP DOWN THE BRAKE PRESSURE; RESETTING THE PARKING BRAKE; 3 TIMES PRIOR TO GATE DEP FOR MAINT TO TROUBLESHOOT. DURING OUR DEBRIEF; THE CAPT INDICATED HE WAS FOCUSED ON THE BRAKE PRESSURE AND HYD PRESSURE GAUGES DURING DISCONNECT FROM THE TUG. I WAS HEADS DOWN AFTER START GETTING THE CLOSEOUT FROM ACARS. THIS EVENT RE-EMPHASIZED THE NEED TO STAY FOCUSED ON THE TASK AT HAND. AFTER LNDG; THE CAPT CALLED THE PUSH CREW TO CONDUCT A PHONE DEBRIEF. SUPPLEMENTAL INFO FROM ACN 789375: UPON ARR; WE NOTED THAT THE L BRAKE PRESSURE CONTINUED TO DEPLETE RAPIDLY BEYOND LIMITS AND MAINT WAS CALLED FOR A THIRD REPEAT OF THE PREVIOUS BRAKE PROB PIREP. ACFT WAS JUST SIGNED OFF BY MAINT PRIOR TO PUSHBACK DUE TO A REPEAT PIREP ON THE L BRAKE SYS RAPID BLEED DOWN OF PRESSURE. AS PUSHBACK WAS COMPLETED; I THOUGHT I HAD SET THE BRAKES AND GAVE THE TUG PERSON AN ALL CLR TO DISCONNECT. THE L ENG WAS COMING UP TO IDLE AS WE MONITORED THE SYS. I WAS CONCENTRATING ON THE BRAKE PRESSURE AND AS I LOOKED UP; I NOTICED THE ACFT WAS STARTING TO ROLL FORWARD. I IMMEDIATELY APPLIED THE BRAKES AND STOPPED NOTICING THAT THE PUSH CREW WAS CLRING THE AREA. IN MY SYS SCAN FOR A 1-ENG TAXI; MY DISTR WITH THE BRAKE PRESSURE READING HAD CAUSED ME TO EITHER NOT SET THE BRAKES PROPERLY TO THE DETENT OR MY CONTINUED BRAKE PEDAL PRESSURE MAY HAVE CAUSED THE BRAKES TO RELEASE EARLY ALLOWING THE ACFT TO ROLL. BEING MORE ATTENTIVE TO THE TASK AND NOT BEING FIXATED ON A SYS WOULD NOT HAVE COMPROMISED SAFETY.