B737 FLC PUSH BACK WITH PAX NOT SEATED. FAA INSPECTOR ABOARD INFORMED CABIN ATTENDANT OF NOTICING ERROR.

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PAX BOARDED WHILE COCKPIT CREW COMPLETED BEFORE START CHKLIST; CONTACTED RAMP AGENT ON HEADSET AND AFFIRMED 'A'S' OFF BRAKES SET. EXCUSED MYSELF OFF HEADSET TO SECURE COCKPIT DOOR. FLT ATTENDANT DISENGAGED BUNGEE CORD; HANDED ME NAPKIN WITH PAX COUNT; PUSHING COCKPIT DOOR TOWARD ME. I ASKED IF THEY HAD FOUND A VOLUNTEER TO MOVE SO THAT A LATE BOARDING MOTHER AND CHILD COULD SIT TOGETHER. THEY HAD; SO DOOR WAS SHUT AND WE WERE PINNED IN. SEAT RAISED; DOOR LOCKED; PUSHBACK COMMENCED. ABOUT 10 SECONDS INTO PUSH; FLT ATTENDANT RANG TWICE AND SAID THAT A GAME OF 'MUSICAL CHAIRS' HAD BEGUN. I INFORMED TUG CREW AND SAID TO BE VERY GENTLE -- A PLANE WAS APCHING THE GATE FOR TAXI IN AND DID NOT WANT TO COMPROMISE OUR CLRNC NOR DID I WANT HIM TO PUT ON THE BRAKES AND POSSIBLY CAUSE A PAX TO LOSE THEIR BAL. THE PAX SAT DOWN WITHIN 10 SECONDS AND PUSHBACK WAS COMPLETED. FLT ATTENDANT LATER INFORMED ME THAT AN FAA EMPLOYEE HAD MADE A MINOR ISSUE OF IT AND HAD GIVEN HER HIS BUSINESS CARD. I WOULD LIKE TO POINT OUT THAT WITH OUR CURRENT SECURITY PROCS OF CLOSING AND LOCKING AND PINNING THE COCKPIT DOOR; IF SOMEONE DOES STAND UP OR THERE IS A NEED TO GET IN TOUCH WITH THE COCKPIT; THERE WILL BE A DELAY IN COMMUNICATING THE PARTICULARS OF THE SIT.