AN ALTDEV OVERSHOT WHEN A B737-400 FLC GETS INVOLVED IN AN ERROR CHAIN WHILE DEP PSP; CA.

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OUR ALTDEV OCCURRED BECAUSE OF MANY EVENTS. I NEVER THOUGHT IT WOULD HAPPEN TO ME. THE CHAIN OF EVENTS STARTED WITH THE RECEIPT OF ATC CLRNC. A JUMP SEATER SHOWED UP RIGHT IN THE MIDDLE OF RECEIVING IT; A COMPANY CHK AIRMAN. THE CAPT THOUGHT THE CLRNC WAS TO 15000 FT; WHEN IT WAS ACTUALLY TO 13000 FT. THE CAPT SET 15000 FT IN THE ALT ALERTER. I DIDN'T CATCH THE MISTAKE. THE JUMP SEATER HELPED ME GET A JOB WITH THE AIRLINE; AND I WAS DISTRACTED TALKING WITH HIM. THE NEXT EVENT IN THE CHAIN WAS OUR PRE-DEP SCAN. THE CAPT DID THE SCAN; I WAS XCHKING. AS WE GOT TO THE ALT (DURING THE SCAN); THE 'A' FLT ATTENDANT ASKED US IF WE NEEDED ANYTHING. WE SKIPPED OVER THE ALT IN THE SCAN. THE NEXT EVENT IN THE CHAIN WAS JUST AFTER TKOF. THERE WAS A CESSNA ENTERING A STRAIGHT-IN DOWNWIND DSNDING OUT OF 4200 FT. WE WERE DISTRACTED LOOKING FOR THE ACFT. CHKED IN WITH DEP AND READ CLBING TO 15000 FT. DEP CTL ACKNOWLEDGED AND IMMEDIATELY CALLED TFC AT 2-3 O'CLOCK POS. WE SAW THE ACFT PASSING OFF OUR R. NEXT EVENT WAS RECEIPT OF ZLA FREQ. WE WERE GIVEN 126.35. I READ BACK 136.35; WAITED FOR RESPONSE IF INCORRECT; AND SWITCHED THE RADIO. WE TRIED TO CONTACT ZLA TWICE ON 136.35. WE SWITCHED BACK TO PSP DEP AND RECEIVED ZLA ON 126.35. AND 'BY THE WAY; YOU ARE ONLY CLRED TO FL130;' WE WERE PASSING THROUGH 13500 FT. WE LET THE ACFT REACH 13800 FT ON THE LEVELOFF BACK TO 13000 FT. WE CHKED IN WITH ZLA AND CONFIRMED LEVELING OFF BACK AT 13000 FT. WE THEN WERE GIVEN A CLB TO FL220. THERE WAS NO TFC CONFLICT. I PRIDE MYSELF ON DOING MY JOB WELL; FOLLOWING EVERY RULE AND PROC IN PLACE. THE PROCS ARE THERE TO STOP THIS FROM HAPPENING. THE HOLES IN THE CLASSIC 'SWISS CHEESE' INCIDENT/ACCIDENT MODEL JUST LINED UP. ALL WE NEEDED WAS AN MEL'ED TCAS SYS AND ANOTHER ACFT COMING THE OTHER WAY. IT COULD HAVE BEEN UGLY. AS I SAID BEFORE; I NEVER THOUGHT IT WOULD HAPPEN TO ME.