747-400 CREW HAD ALTDEV ON A MISSED APCH IN LAX CLASS B AIRSPACE.

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ON APCH TO LAX DEPARTING SMO; 070 DEG HDG; 7000 FT; CLRED TO 3500 FT. ASKED IF WE HAD ARPT. SAID NO DUE TO HAZE LAYER. AT 6000 FT ATC GAVE US A 220 DEG HDG INSIDE MARKER. RECOGNIZED AT ABOUT 3000 FT THAT WE WOULD BE TOO HIGH TO LAND. ADVISED TO CONTINUE DSCNT TO 2000 FT AND CONTINUE TO VOR. DSNDED TO ABOUT 2200-2300 FT; THEN DURING FLAP RETRACTION WENT BACK TO 2500 FT BEFORE CORRECTING BACK TO 2000 FT. THEN CLRED TO 3000 FT AND A L TURN FOR ANOTHER APCH. WE ERRED IN ACCEPTING TOO CLOSE OF A TURN IN FOR INITIAL APCH. IN THE FUTURE; I WOULD SUGGEST FO LEAVE AUTOPLT ON TO MANAGE WORKLOAD UNTIL LNDG ASSURED. FATIGUE FROM 14+ HR FLT MAY HAVE BEEN A FACTOR AS WELL AS ATC TRYING TO DO VISUALS WITH A HVY HAZE LAYER FROM 2000-4000 FT. SUPPLEMENTAL INFO FROM ACN 498121: ATC VECTORED US INSIDE THE OM. WE FINALLY SAW RWY 25L; DETERMINED TOO HIGH FOR SAFE APCH AND RPTED GOING AROUND. ATC TOLD US TO FLY 250 DEG HDG AND DSND TO 2000 FT. DSNDING THROUGH 2500 FT; WE WERE RAISING FLAPS AND TURNING TO NEW HDG 160 DEGS WHEN AIRPLANE INADVERTENTLY CLBED TO 2500 FT. WE IMMEDIATELY RESTORED DSCNT TO 2000 FT AND TURNED TO NEW HDG 070 DEGS. THE INCIDENT TEACHES BETTER USE OF FLT MODE ANNUNCIATIONS AND BETTER ATTN TO AIRPLANE PITCH CHANGE DURING FLAP RETRACTION. ALSO TEACHES BETTER JUDGEMENT IN ACCEPTING VECTORS TO VISUAL IN HAZY FLT CONDITIONS.