AN ACR FLC FLYING B737-300 TO CMH INCORRECTLY SET THEIR ALTIMETERS RESULTING IN AN ALTDEV FROM THAT ASSIGNED.

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FO SAID CTR GAVE US 30.11 ALTIMETER. I SET THAT; AND BEFORE I HAD A CHANCE TO VERIFY THAT WITH ATIS; CMH APCH SAID THEY SHOWED US 300 FT LOW (TFC 2 MI; 10 O'CLOCK; 9500 FT. I HAD TO TURN ALT WINDOW UP TO 10300 FT TO GET VERT SPD TO START US UP). THEY ISSUED ALTIMETER OF 29.67; OR ROUGHLY 500 FT OFF. IN THE ATTEMPT TO CLB; WE THEN OVERSHOT JUST AS WE ENTERED A CELL AND UPDRAFT. GOT THE ALT UNDER CTL; AND VECTORED TO ILS. THEY CLRED US TO INTERCEPT TOO LATE; VOR/LOC DIDN'T CAPTURE. I GAVE IT A COUPLE OF SECONDS; AND THEN TURNED OFF AUTOPLT AND HAND FLEW BACK TO CAPTURE AND FLEW ON IN BY HAND. I SHOULD HAVE STARTED HAND FLYING EARLIER; WHEN I FIRST HAD TROUBLE GETTING ACFT TO CLB BACK UP TO CORRECT ALT WHEN WE RESET ALTIMETERS. PRIOR TO THAT EVEN; I WAS BEHIND; CATCHING UP WITH RERTE AND FLURRY OF ALT CHANGES AND TRUSTED FO TOO MUCH WHEN HE GAVE ME THE ALTIMETER SETTING. I KNEW I SHOULD XCHK THE NUMBER WHEN I SET IT; BUT WE GOT A FLURRY OF REVISED ROUTINGS AND VECTORS THAT KEPT ME VERY BUSY; AND WE REACHED LEVELOFF BEFORE I GOT THE XCHK COMPLETE. ALSO; IT WAS THE FIRST LEG WITH A NEW FO; AND WHILE MOST ARE VERY STRONG AND METHODICAL; AND I TEND TO TRUST THEM UNTIL PROVEN WRONG; THIS FO HAS PROVEN TO BE LACKADAISICAL AND SLOPPY IN HIS THINKING AND PROCS. THIS WAS A WAKE-UP CALL FOR ME TO KEEP A CLOSER XCHK; AND TO VERY METHODICALLY XCHK CRITICAL DATA EVERY TIME -- EVEN IF VERY BUSY.