LEARJET 31 FO WAS SLOPPY IN MAINTAINING SPD REDUCTION AND TURNING TO A VECTOR HDG CAUSING ATC TO GIVE A NEW HDG AND ASK FOR THE WINDS ALOFT SPD.

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ON THE LAST LEG OF A LONG DUTY DAY; WE WERE BEING VECTORED BY BOS APCH FOR THE ILS RWY 6 AT BDR. APCH ISSUED A HDG CHANGE (060 DEGS TO 015 DEGS) AND A SPD REDUCTION TO 180 KTS. AS BOTH CAPT AND PNF; I READ BACK 015 DEGS AND THE SPD REDUCTION. THINKING THE PF WAS COMPLYING; I LOOKED DOWN TO SET THE FMS TO THE OM (STANE) AND THEN THE ARPT. THE FO (PF) SUBSEQUENTLY ASKED IF 015 DEGS HAD BEEN SET ON THE DIRECTIONAL GYRO. I HAD NOT SET THE BUG AND ASKED IF 015 DEGS WAS INDEED THE NEW HDG. WHEN NEITHER OF US COULD CONFIDENTLY SAY IT WAS; I QUERIED ATC ABOUT THE HDG AND WAS TOLD TO TURN TO 330 DEGS AND WERE WE AT 180 KTS. I REPLIED 187 KTS ON THE SPD AND BUGGED 330 DEGS ON BOTH DIRECTIONAL GYROS (COMMON BUG FOR BOTH). I THEN RETURNED TO THE FMS TO SET STANE AS WE WERE IMC AND THEN STARTED TO SET THE LOC IN BOTH NAVS WITH THE INBOUND COURSE (060 DEGS). LOOKING UP AT OUR AIRSPD; I NOTICED WE WERE GETTING FAST AND BROUGHT THE THROTTLES BACK TO REGAIN 180 KTS. AT THIS TIME WE WERE IN A DSCNT AND ATC ASKED FOR THE WINDS AT OUR ALT. THERE WERE NO TARGETS WITHIN A 10 MI RING ON TCASII AND WE HEARD ONLY 1 OTHER ACFT ON FREQ N OF BDR. WE WERE VECTORED ONTO THE ILS AND LANDED WITHOUT INCIDENT. ATTRIBUTING TO THE CONFUSION IN THE COCKPIT WAS FATIGUE AS WE WERE ENDING A LONG DAY; WE HAD OUR CLRNC CHANGED 4 TIMES ENRTE FROM IAD TO BDR WHICH HAD COMPOUNDED OUR WORKLOAD AND MY FAILURE TO MORE CLOSELY MONITOR THE LOW TIME (TURBINE) FO WHILE HE WAS FLYING. APCH HAD ASKED US FOR THE WINDS AT OUR ALT TWICE AND THE OTHER ACFT N OF BDR WHAT HIS WINDS WERE; LEADING US TO BELIEVE THAT WE MAY HAVE BEEN TOO SLOW TO COMPLY WITH HIS DIRECTIVES -- MOST NOTABLY THE AIRSPD.