ACFT NOT AIRWORTHY TO CARRY ALL SEATED PAX.

Narrative

I IMPROPERLY MISREAD THE ACFT MEL LOG. ONE OF THE PAX SEATS WAS INOP -- APPARENT SPRING TO SEAT BUCKLE DISCONNECT WAS MISSING. FLT CONTINUED FROM BOS-BDL WITH A PAX OCCUPYING THE BROKEN SEAT. I DIDN'T REALIZE THE SEAT WAS BROKEN UNTIL AFTER POSTFLT. THE CONFUSION HAPPENED WHEN THE CREW WAS TOLD TO SWAP ACFT IN LITTLE TIME. THUS; OUR EFFORTS WERE RUSHED; AND THE BROKEN SEAT WAS NOT REALIZED WHILE TRYING TO DEPART ON TIME WITHIN SCHEDULE. PROBLEM AROSE: ON ACFT SWAP -- RUSH SIT TO PREFLT AND PREPARE NEW ACFT ON TIME. DISCOVERED: AFTER THE POSTFLT. HUMAN FACTOR: MY WILLING TO DEPART ON TIME BUT FAILURE TO FULLY READ UNDERSTAND MEL COMPLETELY AND FORGOT ABOUT BROKEN SEAT. CARELESS MISTAKE. SUPPLEMENTAL INFO FROM ACN 287440: THE CAPT WAS A FIRST TIME PIC WITH 3 MONTHS EXPERIENCE AND I AM A 3 MONTH NEW HIRE FO. THE AFFECTED SEAT SHOULD HAVE BEEN BLOCKED 'DO NOT OCCUPY' AND THE MEL INOP STICKER SHOULD HAVE BEEN PLACED IN A MORE VISIBLE POS WITH REGARDS TO THE COCKPIT LIGHTING AS DIRECTED BY THE MEL PROC.