CREW SETS ALT ALERTER INCORRECTLY AND OVERSHOOTS ALT ASSIGNED.

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WE HAD A CLRNC FOR THE PHILLY 6 DEP FROM PHL WHICH HAS A PUBLISHED STANDARD ALT OF 5000 FT. CLRNC ISSUED US THE SID WITH AN AMENDED ALT OF 4000 FT FOR OUR SHORT FLT TO RDG. ON DEP WE ACCIDENTALLY CLBED TO 5000 FT AND DEP CAUGHT US; TAKING US BACK DOWN TO 4000 FT. HOW DID THIS HAPPEN? 1) THE STORM WINDOW ON MY SIDE OF THE COCKPIT WAS SLOW TO SEAL AS WE PRESSURIZED. I WAS DISTRACTED BY THE NOISE AND TRYING TO TAKE CARE OF THAT. 2) THE FO (WHO WAS THE PF) WAS BRAND NEW WITH ABOUT 100 HRS TOTAL IN THE AIRPLANE AND HAD NEVER BEFORE FLOWN IN THE NE. I'VE CAUGHT ALL HIS PREVIOUS MISTAKES SO FAR; BUT MY COMPANY PAIRS CREWS TOGETHER FOR AN ENTIRE MONTH. THIS IS THE 10TH DAY I'VE FLOWN WITH HIM AND THE INCREASED WORKLOAD IS TAKING A TOLL. 3) THE PAX HAD BEEN BROUGHT TO THE PLANE UNEXPECTEDLY EARLY; CAUSING US TO FEEL RUSHED DURING OUR PREFLT DUTIES. THIS RESULTED IN THE WRONG ALT BEING SET IN THE ALT ALERTER. WE DO THIS DEP ALL THE TIME TO 5000 FT SO THE MISSET ALERTER DIDN'T STAND OUT AS BEING WRONG TO ME.