IN QUICK RESPONSE TO ATC TO STOP CLB AND RETURN TO AN LOWER ALT FOR TFC; THE FLC OF A MD80 IN DOING THAT; IMMEDIATELY UPON RAPID THROTTLE RETARDING HEAR SEVERAL 'POP' SOUNDS; SIMILAR TO AN ENG COMPRESSOR STALL. HOWEVER; ALL ENG INDICATIONS WERE NORMAL AFTER THE INCIDENT; SO THE FLT WAS CONTINUED TO DEST WITH NO PROBS OR NOISES.

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ALTHOUGH I FEEL WE (COCKPIT CREW) WERE CORRECT IN OUR HANDLING OF THE SIT; THIS OCCURRENCE IS BEING WRITTEN UP DUE TO A CONFLICTING FAA SAFETY INSPECTOR'S DECISION. SAFETY INSPECTOR BOARDED OUR FLT IN ATL TO CABIN INSPECT OUR CABIN CREW TO IAD. APPROX 20 MINS INTO AN 1 HR 15 MIN FLT; WE WERE CLBING FROM FL280 TO FL290. THE FLT CONDITIONS CONSISTED OF CONTINUOUS MODERATE TURB AND 7/10 OF THE ATL AREA IN TSTMS. ZTL CLRED US TO DSND QUICKLY BACK TO FL280 FOR TFC. AT THE TIME THE AUTOPLT; AUTOTHROTTLES AND ENG HEATERS WERE ON AS THE CAPT (PF) INITIATED THE DSCNT WITH THE VERT SPD WHEEL; THE AUTOTHROTTLES RETARDED AND THEN WE HEARD SEVERAL QUICK LOUD 'POPS' THAT LASTED A TOTAL OF 2 SECONDS. THE #1 FLT ATTENDANT CAME UP AND ASKED WHAT THE NOISE WAS. WE SAID THAT IT MIGHT HAVE BEEN A COMPRESSOR STALL; HOWEVER; THERE WAS NEVER ANY ABNORMAL ENG OR ANY OTHER INDICATION. THE AUTOTHROTTLES REMAINED ENGAGED. THEY WILL DISENGAGE WITH ANY ABNORMAL FLUX IN PWR. SHE SAID THAT ALL WAS OK IN THE CABIN; EXCEPT THAT EVERYONE WAS WONDERING WHAT THE NOISE WAS. THE #1 FLT ATTENDANT CAME BACK UP APPROX 2 MINS LATER AND SAID THAT THE FAA INSPECTOR WANTED TO KNOW WHAT WAS GOING ON IN THE COCKPIT. WE TOLD HER THAT ALL WAS OK. THE CAPT MADE AN INFORMATIVE PAX ANNOUNCEMENT. THIS WAS ONLY A BRIEF ONE-TIME OCCURRENCE WITH NO ABNORMAL INDICATIONS; WE CONTINUED. OUR ABNORMAL SECTION OF OUR AOM INSTRUCTS ON HOW TO STOP THE 'POPPING' NOISE AND SECURE AN ENG IF UNABLE. IT DOES NOT INSTRUCT TO RETURN OR LAND AHEAD OF SCHEDULE. WHEN WE ARRIVED AT IAD WITHOUT ANY FURTHER ABNORMALITIES; THE FAA INSPECTOR QUERIED TO WHY WE DID NOT RETURN TO ATL. WE STATED THAT THERE WAS NO ABNORMAL INDICATIONS WHICH WOULD GO ALONG WITH THE PROC FOR A COMPRESSOR STALL. THE CAPT FELT BEST TO CONTINUE AND NOT RETURN TO THE TURB IN ATL WITH A 'GOOD' ACFT. THE INSPECTOR SAID HE DISAGREED AND STATED THAT HE WAS WRITING UP A RPT. I FEEL THE INSPECTOR SHOWED TOTAL LACK OF RESPECT FOR THE CREW AND ITS KNOWLEDGE AND PROFESSIONALISM -- NOR THE CAPT'S DECISION.