AN LTT CAUSED AN AIRBORNE CONFLICT WHEN THE FLC FAILED TO TURN TO THE MISSED APCH HDG DURING A MISSED APCH.

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BOTH THE CAPT (PNF) AND MYSELF (PF) WERE UNAWARE OF ANY PROBS OR 'TFC CONFLICTS' CONCERNING OUR FLT FROM SMO TO LAX. IT WAS NOT UNTIL BEING ON THE GND AT LAX AT FBO AND BEING VISITED BY MR. FAA INSPECTOR WHO SAID HE WAS CHARGED WITH COLLECTING OUR INFO CONCERNING A POSSIBLE TFC CONFLICT WHICH HE THOUGHT HAD SOMETHING TO DO WITH A TURN TO A WRONG HDG. HE ALSO DID NOT KNOW WHETHER THE ERROR WAS ATC OR THE CREW'S ERROR. HE MERELY WAS AT THIS POINT COLLECTING DATA. BOTH THE CAPT AND MYSELF THOUGHT THE VISIT BY MR. INSPECTOR WAS A STANDARD FAA 135 RAMP CHK. THE CAPT AND I BOTH EXPRESSED OUR SURPRISE TO MR. INSPECTOR AND STATED TO HIM WE WERE UNAWARE OF ANY CONFLICT AND THAT THE ONLY UNUSUAL PART OF THE FLT FROM 'MISSED APCH' AT SMO TO VECTORS TO THE ILS RWY 24R AT LAX WAS A CLRNC TO 'TURN R (A HDG; I DO NOT RECALL); IMMEDIATELY.' I REMEMBER THE TURN BECAUSE IT WAS IN EXCESS OF 180 DEGS. JUST PRIOR TO THE CLRNC 'TURN R (A HDG); IMMEDIATELY' WE RECEIVED THE CLRNC 'MAINTAIN 180 IAS.' OUR RESPONSE TO MR. FAA INSPECTOR WAS THAT WE FELT ATC WAS TRYING TO FIT US INTO THE TFC FLOW FOR LAX AFTER GOING 'MISSED' AT SMO AND WAS UNABLE TO DO SO WITH THE CLRNC 'MAINTAIN 180 IAS;' WHAT SHORTLY FOLLOWED WAS THE CLRNC TO 'TURN R (A HDG); IMMEDIATELY.' THE FOLLOWING ARE MY THOUGHTS BASED ON MY RECOLLECTIONS. WHEN WE ARRIVED AT THE MISSED APCH POINT; IN THIS CASE THE SMO VOR; PREVAILING CONDITIONS WERE IMC. AT ABOUT THE 2.0 DME FIX I HAD THE RWY ONLY MOMENTARILY. I WAS NOT IN A POS TO MAKE A NORMAL LNDG AND HAD I HAVE BEEN I DO NOT BELIEVE IT WOULD HAVE REMAINED VFR FOR THE LNDG. I DID NOT EXPECT THAT MISSED APCH; THOUGH WE BRIEFED THE PLATE; BECAUSE OF ATIS; AND AS I HAVE LEARNED; ATIS CAN BE WRONG AND IN THIS CASE IT WAS. I WAS NOT THINKING 'MISSED' AND SHOULD HAVE BEEN. I DO NOT RECALL EVER INTERCEPTING THE 250 DEG RADIAL OFF OF SMO; THE MISSED APCH PROC. AT THE MISSED APCH POINT I ADDED TKOF THRUST; CALLED FLAPS 20 DEGS; MY CAPT CALLED POSITIVE RATE; AND I CALLED GEAR UP. I CONTINUED TO CALL FOR MY AIRPLANE TO BE CLEANED UP WHEN APPROPRIATE AND TURNED TO INTERCEPT THE MISSED APCH PROC. AT THIS POINT IT WAS VERY BUSY ON THE FLT DECK. THE CAPT WAS INFORMING ATC OF OUR MISSED APCH; AN ALT OF 2000 FT WAS ASSIGNED; UNLIKE THE MISSED APCH PROC WHICH CALLED FOR 4000 FT. BEFORE INTERCEPTING THE 250 DEG RADIAL OFF OF SMO WE BEGAN RECEIVING VECTORS. AGAIN; IT WAS VERY BUSY ON THE FLT DECK. HDG CHANGES; ALT CHANGES; AIRSPD CHANGES. THE CAPT WAS ON AND OFF OF THE #1 COM WITH ME GUARDING. THE PURPOSE OF THE CAPT BEING OFF: RECEIVING ATIS FOR LAX; AND ARRANGING TRANSPORT FOR OUR PAX AT LAX; FBO. ABOUT 5 MINS INTO THE 20 MIN OR LESS FLT FROM SMO TO LAX; WE RECEIVED THE CLRNC 'MAINTAIN 180 IAS' FROM ATC. SHORTLY AFTER THAT CLRNC WE RECEIVED THE CLRNC 'TURN R (A HDG); IMMEDIATELY.' THE CAPT WAS OFF THE #1 COM WHEN I RECEIVED THE CLRNC. I BEGAN THE TURN AND INFORMED HIM OF MY ACTIONS AND WHY. THE REST OF THE FLT WAS UNEVENTFUL; OR AS NORMAL AS ANY OTHER MISSED APCH AND VECTOR TO A LOW ILS APCH. WE LANDED AND TAXIED IN AND OUR PAX WERE ON THEIR WAY.