LGT GIVEN DEP CHANGE ALONG WITH TKOF CLRNC. HDG DEV.

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ATC 'LAST MIN' CHANGE AND MY FAILURE TO DEMAND TIME FOR 'COMPLETE' CREW COORD CONTRIBUTE TO MAJOR NAV ERROR. TAXIING INTO POS; CLRED FOR TKOF RWY 31L JFK (KENNEDY 6 DEP -- CANARSIE CLB) FO'S LEG. TWR NOW CHANGES DEP TO BRIDGE CLB. WE ADVISE ATC WE WILL NEED DELAY TO REVIEW NEW DEP. ATC SOUNDING CONFUSED AND HURRIED VOLUNTEERS NDB FREQ OF 414 KHZ; THEN HDG OF 220 DEGS. QUICK TUNE OF ADF BY FO AND I SHOWS ADF NEEDLES POINT STRONGLY TO 070 DEGS BTS. ASSUMING FO IDENTS NDB; I SCAN DEP TEXT. 'DIRECT OGY NDB THEN FLY 220 DEGS; MAINTAIN 5000 FT.' I MISS 'TURN L' TO R OF TRANSITION NAME. AFTER HDOF TO DEP CTL; ATC ADVISES ACFT HDG WRONG DIRECTION. I RE-TUNE ADF FROM APPROX 408 KHZ AND IDENT. ERROR AND SITUATION NOW OBVIOUS. ATC ASSIGNS 070 DEG HDG. NO CONFLICT OCCURRED BUT POTENTIAL OBVIOUS. THIS INCIDENT REMINDED ME OF OTHER DEPS AND MANY ARRS WHEN LAST MIN CHANGES CREATED AN ENVIRONMENT FOR A MAJOR ERROR. THE ARR BEING THE MOST RIPE FOR DISASTER. EXAMPLE: ATIS REF OF EXPECTED APCH IS BRIEFED BY CREW AND SUBSEQUENTLY CHANGED BY APCH CTL (OR; IN SOME CASES; THE CTL TWR) MAKING A COMPLETE BRIEFING AND MIND SET CHANGE BY CREW DIFFICULT AT BEST. I HAVE MADE THE ESSENTIAL CHANGES IN MY PROCS AS CAPT TO NEVER ALLOW THIS KIND OF THING TO HAPPEN AGAIN.