POTENTIAL CONFLICT BTWN A CLBING B767-300ER AND OTHER TFC; DURING A DEP PROC; WITH THE WRONG HDG PLACED INTO THE HDG MODE CTL; 50 NM N OF MKK VOR; HI.

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DURING CLBOUT ENRTE FROM HNL; WE WERE GIVEN MULTIPLE VECTORS. IN SHORT ORDER; HDG 80 DEGS; THEN 60 DEGS; THEN 40 DEGS; THEN WHAT I THOUGHT AS 335 DEGS. I BELIEVE THE CAPT RESPONDED TO THE LAST HDG ASSIGNMENT; ALTHOUGH HE DOES NOT REMEMBER DOING SO ( 40 DEG HDG IS THE LAST HDG HE REMEMBERS ACKNOWLEDGING). ATC DID NOT CORRECT; OR REPEAT OUR HDG ASSIGNMENT. ROLLING OUT OF THE TURN; ATC ASKED US WHAT HDG WE WERE TURNING TO (WE RESPONDED 335 DEG); THEN TOLD US WE WERE ASSIGNED 35 DEG. JUST AFTER PASSING FL202; ATC THEN TOLD US TO LEVEL OFF AT FL200. WE RESPONDED; AND RETURNED IMMEDIATELY TO FL200. ATC ALSO HAD US HOLD HDG 335 DEGS FOR A COUPLE MINUTES MORE FOR TFC. DURING THIS TIME; WE RECEIVED A MOMENTARY TA; AND I BELIEVE THE CTLR VECTORED THE OTHER ACFT AROUND US. A NEW VECTOR WAS ASSIGNED; AND WE WERE ON OUR WAY WITHOUT FURTHER DISCUSSION WITH THE CTLR ABOUT THE EVENT. IT APPEARS THAT UNLESS THE CTLR GAVE US THE WRONG HDG; I PROBABLY HEARD THE WRONG HDG (335 DEG HDG INSTEAD OF 35 DEG HDG); AND SET THIS IN THE HDG SELECTOR. I BELIEVE THE CAPT ACKNOWLEDGED THE HDG GIVEN (35 DEG HDG); AND DID NOT NOTICE THE DIFFERENT HDG SELECTED. UNABLE TO HEAR HIS RESPONSE THROUGH THE HEADSET; I DID NOT DETECT A HDG DIFFERENT THAN THE ONE I SELECTED. IT WAS A VERY BUSY COCKPIT; ESPECIALLY FOR THE CAPT. THE CTLR WAS PROBABLY ALSO BUSY AS TO ALLOW US TO TURN 60 DEGS PAST OUR ASSIGNED HDG. WITHOUT REVIEWING THE TAPES; THIS EVENT IS LIKELY MY OWN FAULT. IT WAS AN HONEST MISTAKE OF HEARING A DIFFERENT HDG THAN THAT GIVEN. NORMALLY; WHEN THERE IS A QUESTION OF UNCLR OR QUESTIONABLE INSTRUCTIONS; I WOULD GET CLARIFICATION FROM ATC. AT THE TIME; I DID NOT PERCEIVE THE NEED. THERE WAS NO INTENTIONAL DEVIATION FROM ATC'S INSTRUCTIONS OR NORMAL OPERATING PROCS. THERE WILL BE TIMES WHEN HUMAN FACTORS (MISCOM) WILL INTERFERE WITH AN OTHERWISE PERFECT GAME PLAN. I WILL TRY HARDER TO REDUCE THIS RISK. I WISH THAT BTWN THE 3 PERSONS INVOLVED; ONE OF US DISCOVERED THE PROB BEFORE IT BECAME A PROB. FOR THIS PART; I DO HAVE ONE THING I WOULD RECOMMEND. WHENEVER WE ARE GIVEN NEW ALTS; AS A NORMAL OPERATING PROC; WE CONFIRM THE SELECTED VALUE WITH THE OTHER PLT. THIS SEEMS TO WORK WELL AS A SAFETY NET IN ADDITION TO THE NORMAL READBACKS OF ATC CLRNCS. AS A PNF; I NORMALLY DO THE SAME FOR HDG CHANGES TO MAKE SURE THE PF IS ON THE SAME PAGE. THIS MIGHT BE A GOOD PRACTICE TO ACCEPT AS A NORMAL OPERATING PROC. SUPPLEMENTAL INFO FROM ACN 575553: ON CLBOUT FROM HNL; I WAS PERFORMING PNF DUTIES; FO WAS PF. ON HAND-OVER FROM DEP TO CTR; WE WERE GIVEN 60 DEG HDG. AFTER CONTACTING NEW FREQ; WE WERE GIVEN 40 DEG HDG. I PUT THIS INTO MCP; AND AUTOPLT INITIATED THE TURN. I THEN TURNED MY ATTN TO PNF DUTIES -- GROSS ERROR CHK; ETOPS WX REQUEST; PRINTING; AND REVIEWING SOME AFTER DOWNLOAD. THERE WAS ALSO A QUALIFIED FO IN THE JUMPSEAT; WHICH ALSO CONTRIBUTED TO THE GENERAL SENSE OF WELL BEING.