A B737-200 FLC STARTS A WRONG RWY APCH AFTER A MISUNDERSTANDING ABOUT THE RWY ASSIGNMENT AND A FLUCTUATING LOC NEEDLE; 25 MI S OF SDF; KY.

Narrative

AFTER INITIAL CHK-IN WITH APCH CTL AND ASKING FOR DEVS TO THE SW FOR WX; MY NEW COPLT AND I BELIEVE WE WERE TOLD TO EXPECT RWY 35L. AFTER SWITCHING TO ANOTHER APCH FREQ WE WERE GIVEN A POS RPT AND CLRNC TO INTERCEPT THE LOC AND CLRED FROM 4000 FT TO 3000 FT; CLRED FOR THE APCH. MY COPLT READ BACK 'CLRED FOR ILS RWY 35L.' ABOUT THIS TIME MY LOC SIGNAL WAS CYCLING ON AND OFF IN ABOUT A 5 SECOND INTERVAL. I SET UP OUR AUTOMATION TO FLY THE ILS TO RWY 35L. I ASKED THE COPLT TO CALL THE FLT ATTENDANTS TO MAKE SURE THAT THERE WERE NO ELECTRONIC DEVICES ON IN THE CABIN. AFTER LEVELING AT 3000 FT AND ABOUT TO INTERCEPT THE LOC; THE APCH CTLR ASKED 'ARE YOU INTERCEPTING THE RWY 35R ILS?' WE SAID 'NEGATIVE; WE UNDERSTOOD RWY 35L; WOULD YOU LIKE US TO TRANSITION BACK TO RWY 35R?' THE CTLR SAID 'NO' AND ISSUED US A CLRNC TO RWY 35L. IN RETROSPECT; HIGH TASK SIT WITH HVY RAIN AND TSTMS; NEW COPLT; AND TEMPORARY PROBS WITH LOC SIGNALS (WHICH CLRED UP AS WE GOT CLOSER TO LOUISVILLE); I REALIZED THERE WERE 2 PLACES I COULD HAVE CAUGHT OUR ERROR OR MISUNDERSTANDING WHICH OF THE PARALLEL RWYS WE WERE CLRED TO. THE POS RPT 'YOU ARE 10 MI S OF XXX TURN R....' I DID NOT UNDERSTAND THE FIX AND HAD I QUERIED THE CTLR ON THE FIX; WE MIGHT HAVE CAUGHT OUR ERROR. WE COULD HAVE ALSO DONE A BETTER JOB OF LISTENING FOR THE CLRNC. WE HAVE NOT HEARD THE TAPES. LASTLY; ATC SHARES RESPONSIBILITY WITH THE PLTS TO INSURE THE READBACKS ARE CORRECT -- ESPECIALLY AROUND ARPTS WITH PARALLEL RWYS.