A CE560 DEPARTS BUSY BOS; MA; AREA AND HAS AN ALTDEV DURING CLBOUT. AN APCHING ACFT RECEIVES A TCASII RA BECAUSE OF THE FIRST ACFT ALTDEV.

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WE WERE DEPARTING LWM IN IMC; WITH GUSTY SURFACE WINDS AND TURB. OUT INITIAL DEP CLRNC WAS TO 2000 FT. SHORTLY BEFORE REACHING 2000 FT; WE RECEIVED INSTRUCTIONS TO CONTINUE THE CLB. I WAS CONCENTRATING ON ACFT CTL AND MISSED THE CALL; BUT I SAW THE CAPT DIAL IN 6000 FT ON THE ALT ALERTER AND AM POSITIVE I HEARD HIM READ BACK THE ALT ASSIGNMENT AS 6000 FT TO ATC. ATC'S NEXT XMISSION WAS TO ANOTHER ACFT AND THEY DID NOT QUESTION THE READBACK. SHORTLY AFTER LEVELING AT 6000 FT; I HEARD ATC CALL SOMETHING LIKE 'ACFT XX; YOU'RE SUPPOSED TO BE AT 5000 FT; 5000 FT ACFT XX.' I REDUCED PWR AND STARTED TO DSND WHEN THE CAPT SAID 'NO STAY HERE.' HE WAS TRYING TO GET CONFIRMATION; AND SINCE THE FREQ WAS VERY BUSY; I THOUGHT IT MIGHT BE POSSIBLE I MISTOOK A CALL THAT WAS INTENDED FOR ANOTHER ACFT. THE CAPT GOT CONFIRMATION; AND I IMMEDIATELY REDUCED PWR TO IDLE AND CONDUCTED A RAPID DSCNT TO 5000 FT. THIS INCIDENT OCCURRED ON A DEP CLBOUT IN VERY BUSY BOSTON AIRSPACE. VECTORS WERE BEING GIVEN AT THE USUAL RAPID RATE TO MANY ACFT. IN SUCH AN ENVIRONMENT; INSTRUCTIONS GET MISHEARD QUITE FREQUENTLY. THE TECHNIQUE OF READING BACK CLRNCS SHOULD; AND DOES IN MOST CASES; CATCH THESE ERRORS. IN THIS CASE; IT APPARENTLY DID NOT. IN RETROSPECT; I BELIEVE I SHOULD HAVE BEEN MORE AWARE OF THE RADIO XMISSIONS EVEN THOUGH I WAS CONCENTRATING ON ACFT CTL. IN A LESS HECTIC ENVIRONMENT; AND/OR WITH INCREASED SITUATIONAL AWARENESS; I COULD HAVE CAUGHT THE MISTAKE. SUPPLEMENTAL INFO FROM ACN 396712: ZBW THEN SAID TO CLB TO 5000 FT. I READ BACK 5000 FT AND BY MISTAKE DIALED 6000 FT INTO THE ALT PRESELECTOR. AFTER CLBING TO 6000 FT ANOTHER ACFT CLBED FROM 6000 FT TO 6700 FT BASED ON A WARNING GENERATED ON THEIR TCASII. THE FO CONFIRMED 6000 FT IN ACCORDANCE WITH OUR SOPS. AFTER THE INCIDENT I ASKED HIM WHAT HE HEARD AND HE SAID THAT HE REALLY WASN'T PAYING ATTN TO THE RADIO CALLS. WE BOTH SHOULD HAVE PAID CLOSER ATTN TO THE TASK AT HAND TO AVOID THIS POTENTIALLY DANGEROUS SIT.