HS25 FLC DEV. ALTDEV ALT OVERSHOT. WRONG ALTIMETER SETTING; HAD QNE INSTEAD OF QNH. MISSED ALTIMETER SETTING PROC AT FL180.

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WE HAD AN ATC CLRNC TO DSND FROM APPROX FL220 TO 10000 FT IN ABOUT 2 MINS. I WAS CONCENTRATING ON THE DSCNT; BRINGING BACK ALL PWR; PUTTING OUT FULL AIR BRAKES AND ENSURING AIRSPD WAS AS HIGH AS POSSIBLE WITHOUT OVERSPDING. I REACHED 10000 FT AND LEVELED OFF. ATC TOLD US TO CLB TO OUR ASSIGNED ALT OF 10000 FT WHICH WAS EXACTLY WHERE I WAS. WE TOLD HIM 'LEVEL AT 10000 FT' AND HE SAID CHK ALTIMETER. I HAD FORGOTTEN THE TRANSITION CHK AT FL180 AND THUS FORGOT TO RESET THE ALTIMETER. FURTHERMORE; THE ALTIMETER SETTING GIVEN TO US ON THE DSCNT WAS 29.72 AND IT SHOULD HAVE BEEN 29.53. A MIN LATER WE WERE ASKED WHICH RADIAL WE WERE ON TO SMO. WE REPLIED THE 262 DEG RADIAL. HE ASSIGNED US A HDG AND THEN AGAIN ASKED US WHICH RADIAL. WE TOLD HIM WHICH RADIAL AND ALSO SAID WE WERE ASSIGNED HDG. THE WINDS WERE STRONG THAT DAY; SO HE REASSIGNED A NEW HDG. ALTIMETER SETTING WAS A BIG FACTOR IN THIS CASE. YOU DEFINITELY NEED THE ACCURATE ALTIMETER SETTING AND IT IS IMPERATIVE THROUGH YOUR TRANSITION ALT. ALSO; NOT SO MUCH CONCENTRATION ON REACHING A XING RESTR. PERHAPS SIT WOULD HAVE BEEN BETTER TO LET ATC KNOW WE WERE UNABLE TO MAKE THAT QUICK A DSCNT AND THEREFORE WOULD HAVE PROBABLY NOT BEEN AS LIKELY TO OVERLOOK THE TRANSITION CHK. SUPPLEMENTAL INFO FROM ACN 361728: BOTH THE FO AND I WERE SURPRISED WE HAD MISSED THE TRANSITION CHK. I EVEN MORE SO SINCE I NORMALLY READ BACK THE ALTIMETER SETTING TO THE PF DURING THE DSCNT. IT PAYS TO BE EVEN MORE DILIGENT WITH CREWS THAT ARE ACCUSTOMED TO FLYING TOGETHER A LOT.