A B737 CREW MAKES S-TURNS ON FINAL TO LOSE ALT AND MAKES A REQUEST FOR THE OTHER PARALLEL RWY. A TFC CONFLICT NEARLY OCCURS WHEN CREW READS BACK THE WRONG RWY FOR APCH.

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NEW FO IN TRAINING ON DSCNT INTO SLC. B737 HVY (112000 LBS) AND HIGH/FAST FOR ARR. CAPT TOOK ACFT AT 7000 FT MSL AND REQUESTED S-TURNS TO GET DOWN AND CHANGE TO RWY 34L FROM RWY 34R FOR ADDITIONAL SPACE TO GET DOWN. TWR ADVISED TFC; WHICH WE ACKNOWLEDGED; BUT THERE WERE SEVERAL B727'S IN THE TFC AREA AND WE SAW A B727 ON DOWNWIND TO RWY 34L. THE TFC CALLED OUT TO US WAS ON FINAL FOR RWY 34L. WE SAW THAT TFC; CONFIRMED CLRED FOR RWY 34L; AND TWR SAID WE WERE CLRED FOR RWY 34R...RWY 34R AND WE HAD TFC LESS THAN A MI FOR RWY 34L. WE LANDED UNEVENTFULLY ON RWY 34R AND WERE TOLD TO CONTACT TWR (BY PHONE). CAPT CALLED TWR; EXPLAINED HE HAD LET FO GO A LITTLE TOO FAR IN HIS APCH AND GOT HIGH; TOO HIGH FOR THE INTENDED RWY. AS FO; I WAS READY TO GO AROUND AT 3000 FT AGL AND RACK-IT-UP TO EXPERIENCE. THE CAPT REACTED TO THE SIT AND ANTICIPATED TWR'S RESPONSE (EXPECTED RESPONSE) AND QUICKLY ADMITTED GOING AROUND WOULD BE THE PROPER AND PROFESSIONAL ACTION FOR THE SIT. TWR CALLED OUT TFC BUT FAILED TO MENTION 'ON FINAL' OR 'ON DOWNWIND;' WHICH WOULD HAVE HELPED IMMEDIATELY AND KEPT US FROM ASSUMING RWY 34L WOULD BE GIVEN TO US FOR LNDG. A LENGTHY DEBRIEF FOLLOWED AND CAPT MORE CLOSELY FOLLOWED SUBSEQUENT DSCNTS WITH CONSTANT INSTRUCTION/COMMENTS ON FOLLOWING FLTS.