A B737-300 CHK AIRMAN PIC READS BACK AN IMPROPER CLRNC AND SUFFERS A HDG TRACK DEV GOING INTO LAC; CA.

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FLT TO LAX. WX AT LAX WAS DETERIORATING RAPIDLY DUE TO COASTAL FOG. VISIBILITY WENT FROM 5 MI TO LESS THAN 1/2 MI IN LESS THAN 1 HR. ZLA WAS GIVING MAX MACH AND SLOWEST MACH TO ALL ARRIVING ACFT AND TO EXPECT VECTORING. AFTER PASSING DERBB INTXN ON THE SADDE 6 ARR; WE WERE SLOWED TO .70 MACH AND 230 KTS UPON REACHING FL240 AFTER DEPARTING FL290. WHEN REACHING FL240 AND AT 230 KTS; WE WERE GIVEN A 90 DEG HDG CHANGE TO 160 DEGS THEN WITHIN MINS A FREQ CHANGE TO 132.6. WE CHKED I WITH SPD; HDG AND ALT AND WERE TOLD TO PROCEED DIRECT FIM PLAN TO CROSS SYMON AT 12000 FT. REPEATED BACK DIRECT FIM SADDE 6 AND 12000 FT; TO WHICH THE CTLR RESPONDED 'NO; SYMON AT 12000 FT;' SO I REPEATED BACK 'OK; DIRECT SYMON TO CROSS AT 12000 FT.' WE THEN MADE SYMON THE ACTIVE WAYPOINT IN THE FMC EVEN THOUGH WE WERE PREVIOUSLY GIVEN FIM. WE THEN PROCEEDED TO PLAN OUR DSCNT TO CROSS SYMON AT 12000 FT AND 230 KTS. WITHIN A FEW MINS THE CTLR CAME BACK WITH 'ACR X; START YOUR DSCNT NOW.' THERE WAS A LOT OF OTHER SIMILAR ACR CALL SIGNS ON FREQ AND I WAS SURPRISED HE WANTED IT SO SOON AFTER HE HAD ESSENTIALLY GIVEN ME PLT'S DISCRETION TO 12000 FT. IN ANY EVENT; WITHIN A FEW MINS; I WAS QUESTIONED AS TO WAS I DIRECT FIM OR SYMON; IN WHICH I REPLIED SYMON. THE CTLR THEN INFORMED ME I WAS NEVER CLRED DIRECT SYMON; ONLY FIM. I REPLIED 'YOU GAVE ME DIRECT SYMON AND 12000 FT;' AND 'DID WE NEED TO CALL?' CTLR'S RESPONSE WAS 'WILL PULL THE TAPE; CONTACT SOCAL APCH.' I AGAIN ASKED IF WE NEEDED TO CALL AND THERE WAS NO REPLY. UPON ARRIVING INTO LAX; I CALLED CTR AND THE ISSUE WAS RESOLVED. END RESULT -- TOO MUCH TFC; TOO MANY SIMILAR CALL SIGNS; AND POOR RADIO READBACKS.