BE1900 FLT CANCELED AFTER DAMAGED TIRE FOUND ON PREFLT THE DAY AFTER AN IOE FO POSTFLT INSPECTION MISSED THE PROB AT RDG; PA.

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I WAS CONDUCTING IOE WITH A NEW-HIRE FO. IT WAS A BUSY; EVENING SHIFT WITH MANY QUICK TURNS AT UNCTLED FIELDS; FLYING FROM RDG-PIT-ART-OGS-MSS-ART-PIT-RDG. THE WX AT ALL OF THE ARPTS WAS COLD WITH GUSTY WINDS. ALL ARPTS HAD AT LEAST SOME SNOW AND ICE ON THE RWYS; ALTHOUGH BRAKING ACTION WAS DESCRIBED AS 'GOOD' AT MOST OF THE FIELDS. THE FO CANDIDATE DID 4 LNDGS THAT EVENING: 2 AT PIT; 1 AT MSS; AND 1 AT RDG. ALL OF THESE ARPTS WERE RPTING 'GOOD' BRAKING ACTION. BECAUSE OF THE WINDS AND GENERAL EXPERIENCE LEVEL; HE WAS HAVING TROUBLE MAINTAINING RWY ALIGNMENT THROUGHOUT THE APCH AND LNDG; AND REQUIRED MY ASSISTANCE ON SEVERAL LNDGS. AFTER LNDG AT PIT THE SECOND TIME; THE FO NOTED THAT THE ACFT SEEMED TO PULL TO THE R ON ROLLOUT. THE PULLING; HOWEVER; APPEARED TO BE CONSISTENT WITH THE GUSTY XWIND AND THE LNDG GEAR SQUAT SWITCH BRINGING THE PROPS IN AND OUT OF THE GND IDLE POS. AFTER THIS FLT; AS WITH EVERY OTHER; THE FO DID A POSTFLT WALKAROUND LOOKING FOR DAMAGE; AND DIDN'T FIND ANY. WE LANDED LATER THAT EVENING AT RDG AND HAD THE ACFT PUSHED INTO THE HANGAR. ONCE AGAIN; THE FO DID A POSTFLT INSPECTION AND FOUND NO DAMAGE. THE FOLLOWING MORNING; THE CREW ACCEPTING THE ACFT DISCOVERED THE R MAIN GEAR; INNER TIRE WAS FLAT AND DAMAGED. SINCE THE CREW HAD TO CALL IN CONTRACT MAINT; 3 FLTS ENDED UP CANCELING BEFORE THE TIRE WAS REPLACED. OBVIOUSLY; THE FO MADE SOME MISTAKES ON THE POSTFLT INSPECTION BY NOT BEING THOROUGH. HOWEVER; AS PIC; I AM ULTIMATELY RESPONSIBLE FOR THE ACFT AND HAVE TO BE CERTAIN THAT MY FO IS DOING HIS JOB. SINCE HE NEEDED ASSISTANCE IN OTHER AREAS AS WELL; I SHOULD NOT HAVE ASSUMED THE POSTFLT INSPECTIONS THAT HE WAS DOING WERE COMPLETE. KNOWING THAT HIS LEVEL OF EXPERIENCE WAS VERY LOW; I SHOULD HAVE GONE OVER EVERY DETAIL OF THE INSPECTION WITH HIM; EVEN IF IT MEANT DELAYING OUR FLTS. ADDITIONALLY; BECAUSE HE HAD DIFFICULTY WITH HIS APCHS AND LNDG; AND THE GUSTY WIND CONDITIONS; THE PULLING ON TOUCHDOWN DID NOT SEEM UNUSUAL. HAD A MORE EXPERIENCED PLT BEEN FLYING; THE PULLING WOULD HAVE GOTTEN MY ATTN. I SHOULD HAVE PAID MORE RESPECT TO HIS OBSERVATIONS; REGARDLESS OF HIS LEVEL OF EXPERIENCE.