AN ACR B767 FLC EXPERIENCED A MAP SHIFT AND BEGAN TO USE MANUAL CTL OF THE ACFT WITH REF TO THE APCH RAW DATA INFO. HOWEVER; THEY DID NOT REALIZE THAT THE DESIGNATED ALTS AT THE XING POINTS DO NOT NECESSARILY COINCIDE WITH THE GS ALTS AT EACH POINT. THE FLT PATH WAS AS MUCH AS 200 FT LOW AT SOME OF THE XING POINTS.

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ON APCH TO LAX FOR RWY 25L ILS; THERE WAS A MAP SHIFT WHICH MOVED THE TRACK LINE ABOUT 1 MI R OF COURSE. THIS HAPPENED AT APPROX 10000 FT PASSING ARNES INTXN; AND JUST BEFORE CHANGING FROM LNAV TO LOC MODE FOR NAV TRACKING. I DISCONNECTED THE AUTOPLT WHEN THE ACFT STARTED TURNING TO THE DISPLACED TRACK LINE; ENGAGED LOC MODE AND ATTEMPTED TO USE THE FLT DIRECTOR TO INTERCEPT THE INBOUND ILS TRACK. THE FLT DIRECTOR DID NOT PROVIDE PROPER GUIDANCE AND SO I FLEW RAW DATA TO GET BACK ON CTRLINE. THIS OCCURRED IN THE VICINITY OF SEVERAL XING FIXES ON THE APCH; NAMELY SUZZI; GAATE; ETC. AS A RESULT OF DISTR; 1 OR MORE OF THOSE FIXES WERE CROSSED APPROX 200 FT BELOW THE PUBLISHED XING ALTS. THERE WAS NO KNOWN TFC CONFLICT. WHEN ESTABLISHED ON THE LOC; THE FLT DIRECTOR BEGAN TO PERFORM NORMALLY AND THE TRACK LINE SLOWLY MOVED BACK TO A POS CO-INCIDENT WITH THE LOC CTRLINE; BUT THE INDICATED TRACK ON BOTH HSI'S WAS OFF ABOUT 15 DEGS FROM ACTUAL TRACK. ON TOUCHDOWN; THE HSI TRACK SLEWED TO INBOUND COURSE. THE SYS MALFUNCTION WAS WRITTEN UP IN THE ACFT LOGBOOK AND COMPANY MGMNT WAS VERBALLY DEBRIEFED REGARDING THE TRACK SHIFT AND THE MAP SHIFT. THE REASON FOR THE MALFUNCTION IS NOT KNOWN AT THIS TIME. THE SIT WAS EXACERBATED BY THE COMPLEXITY OF THE APCH (LARGE NUMBER OF STEPDOWN FIXES AND NEED TO VERIFY DME DISTANCE OF EACH); ATC SPD RESTR AND COM WITH ATC WHICH WAS RELATIVE TO TFC ON THE RWY 24R VISUAL APCH. IT IS A HIGH WORKLOAD APCH BECAUSE OF THE COMPLEXITY. A LESSER NUMBER OF STEPDOWN FIXES OR ABILITY TO USE GS FURTHER FROM RWY COULD HELP IMPROVE THE APCH. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THAT HE HAD CALLED HIS COMPANY MAINT PERSONNEL TO DISCOVER THE CAUSE OF THE MAP SHIFT AND OTHER PROBS WITH THE FMC; BUT THEY HAD NOT RESPONDED YET. HE SAID THAT HE WOULD CALL ASRS WITH THE INFO WHEN IT WAS AVAILABLE.