B737 FLC MISSET ALTIMETER PASSING FL180 AND OVERSHOT ASSIGNED ALT OF 5000 FT WHILE ON RADAR VECTOR TO PVD.

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PASSING THROUGH FL180; THE ALTIMETER TO BE SET WAS 29.71. PLT AT THE CTLS (CAPT) SET 30.71. AFTER LEVELING OFF AT 4000 FT ON THE CAPT'S ALTIMETER; APCH ASKED OUR ALT. MY INITIAL RESPONSE WAS OUR ASSIGNED '5000 FT.' THAT'S WHAT MY ALTIMETER SHOWED ALONG WITH WHAT THE ALT WINDOW SHOWED. I QUICKLY LOOKED AT THE CAPT'S ALTIMETER AND WAS SHOCKED TO SEE THE 1000 FT DISPARITY. I IMMEDIATELY REALIZED THAT THE CAPT HAD SET THE WRONG ALTIMETER SETTING. HOWEVER; I HAD ALSO REALIZED THAT I MUST HAVE MISSED HIS MISTAKE WHEN COMPLETING THE DSCNT/APCH CHKLIST. AFTER ADVISING APCH CTL; WE MADE AN UNEVENTFUL CLB BACK UP TO 5000 FT AND WAS TOLD THAT THERE WAS NO TFC CONFLICT. LESSONS LEARNED: BECAUSE OF THE 1000 FT SPLIT ON THE ALTIMETER; I ASSUMED THE ALT WAS CORRECT -- IT LOOKED CORRECT! BOTH NEEDLES WERE AT THE 12 O'CLOCK POS IN LEVEL FLT. IN THE FUTURE. I WILL ENSURE THAT I CHK THE NUMERICAL SETTING OF THE ALTIMETER; ALONG WITH THE 1000 FT PRIOR AURAL ALT ALERT -- LIKE I'M SUPPOSED TO DO! I LEARNED A LOT FROM THIS ONE!