FLT CREW OF B737-500 EXPERIENCE EGPWS TERRAIN WARNINGS DURING APCH IN VISUAL CONDITIONS TO CLE. SUSPECT INAPPROPRIATE WARNING THE RESULT OF AN FMS MAP SHIFT SHORTLY BEFORE FINAL APCH.

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ENTERING A MODIFIED BASE LEG FOR A VISUAL TO RWY 24R AT CLE THE CREW NOTICED THAT THERE WAS A SIGNIFICANT MAP SHIFT (AT LEAST 2-3 MI). THE FO WAS STILL IN AUTO. THE CAPT WAS FLYING WITH GS CAPTURE AND LOC CAPTURE AT APPROX 1400 FT. JUST AFTER THE 500 FT CALL; THE EGPWS BEGAN CALLING OUT 'CAUTION TERRAIN; CAUTION TERRAIN.' AT THIS POINT THE CREW CONFIRMED VISUALLY THERE WAS NO TERRAIN PROB AND REALIZING THE CAUTIONS WERE DUE TO THE MAP SHIFT WE CONTINUED THE APCH. DUE TO THE WORKLOAD IN FLYING THE LAST 200 FT TO A XWIND LNDG; THE CAPT WAS UNABLE TO PUSH THE EGPWS TERRAIN OVERRIDE SWITCH; THUS THE GPWS 'TERRAIN; TERRAIN; PULL UP; PULL UP; PULL UP' WAS ACTIVATED. KNOWING THE REASON FOR THE WARNING AND CONFIRMING THE FINAL DSCNT CHKLIST WAS COMPLETE THE CAPT COMPLETED THE LNDG. VERY UNCOMFORTABLE LNDG WITH THE WARNING GOING OFF. LOOKING BACK; GAR MIGHT HAVE BEEN BETTER TO GIVE TIME TO OVERRIDE TERRAIN WARNINGS AND ALLOW FOR A MORE COMFORTABLE APCH TO KEEP BETTER SITUATIONAL AWARENESS. AT GATE; CALLED MR X AND MADE AN INFO RPT AND TALKED TO NEXT CAPT TO ENSURE EVERYONE WAS IN THE LOOP FOR POSSIBLE ACFT DISCREPANCY.