A B767 CREW MAKING A VISUAL APCH TO SLC DSNDED BELOW XING RESTR.

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ON VECTORS FOR A VISUAL APCH TO RWY 16L (RWY THRESHOLD DISPLACEMENT OF 1920 FT) MEN AND EQUIP WORKING ON CLOSED PORTION; 10000+ FT AVAILABLE FOR LNDG; A 'VERY' DIM OR WEAK PLASI ON THE L SIDE OF THE RWY. GS INOP. EXCELLENT CEILING AND VISIBILITY; WE CALLED RWY IN SIGHT AT APPROX IRRON. WHILE ON VECTORS FOR A VISUAL APCH THE CTLR CLRED US TO 8000 FT AND FURTHER CLRED US VISUAL APCH UPON PASSING 9000 FT. LINED UP ON FINAL (LOC CAPTURED). THE APCH CTLR CAME BACK AND CLRED US VISUAL APCH RWY 16L TO CROSS LGOON AT OR ABOVE 7500 FT. I SET 7500 FT IN THE ALT WINDOW. AT LGOON (VIA THE EFIS MAP) RESET THE ALT WINDOW TO THE MINIMUM ALT (10000 FT) AND SET THE VERT SPD TO 700/800 FPM. CONTINUED CONFIGURING THE FLAPS. UPON LOOKING OUTSIDE (RWY -- WEAK PLASI) WE APPEARED TO BE LOW. NO GS AVAILABLE (DISPLACED THRESHOLD). CHKED OUR ALT AT 6900 FT AND THE MAP POS JUST PASSING LGOON (I BELIEVE WE HAD A MAP SHIFT -- +/-3 MI). QUESTIONING WHAT WAS GOING; I VERIFIED OUR POS VIA LOC DME. WE WERE JUST PASSING LGOON (12.3 LOC DME). THE CTLR CALLED AND ASKED WHAT ALT WE HAD UNDERSTOOD TO CROSS LGOON (7500 FT OR ABOVE). I EXPLAINED THAT WE UNDERSTOOD THAT WE WERE TO CROSS LGOON AT OR ABOVE 7500 FT AND FURTHER EXPLAINED THAT WE HAD HAD A MAP SHIFT. HE EXPLAINED THE IMPORTANCE OF THE XING ALT (7500 FT) AND CAUTIONED ABOUT THE ALT FOR FUTURE VISUAL APCH TO RWY 16L. WE APOLOGIZED AND THANKED THE CTLR; WENT TO TWR FOR OUR LNDG CLRNC. I BELIEVE THAT THIS SIT COULD HAVE BEEN PREVENTED IF WE HAD VERIFIED (XCHKED) WHAT WE HAD THOUGHT TO BE LGOON (MAP POS) WITH RAW DATA (LOC DME). IT WOULD HAVE SHOWN THE ERROR (DISCREPANCY -- MAP SHIFT). IT WAS A BUSY COCKPIT BUT THAT WOULD HAVE IDENTED THE MAP SHIFT AND WE COULD HAVE WORKED IT OUT FROM THERE. IT'S NEVER TOO BUSY TO XCHK RAW DATA. IT HAS ALSO MADE ME THINK TWICE ABOUT EFIS GENERATED NAV DATA. VERIFY; EVEN IN VERY VFR CONDITIONS.