PREMIER 1 FLC HAS NAV ERROR DURING TRANS-ATLANTIC XING.

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WE PICKED UP THE CLRNC FOR OUR FLT AND READBACK THE FILED RTEING WITH THE EXCEPTION OF 'OZN' BEING DELETED. A CORRECTION TO THE READBACK WAS GIVEN; CHANGING 61N040W TO 62N040W. WE ACKNOWLEDGED THE CHANGE; DELETED THE ORIGINAL FIX AND ENTERED THE NEW FIX. AT THIS POINT; 1 OF 2 THINGS HAPPENED AND WENT UNNOTICED: EITHER WE RE-ENTERED THE ORIGINAL FIX COORDINATES OR SOMEHOW DID NOT EXECUTE THE CHANGE. AFTER TKOF; I RPTED TO GANDER RADIO OUR ESTIMATE FOR '61N040W;' AS READ FROM OUR 'POS RPT' PAGE ON THE FMS MULTI-FUNCTION DISPLAY. GANDER ACKNOWLEDGED THE ESTIMATE AND ISSUED NO CORRECTIONS. UPON RPTING OUR POS OVER '61N040W;' WE WERE ASKED TO CONFIRM OUR POS AND OUR CLRNC. IT WAS AT THIS TIME THAT WE RECOGNIZED THAT WE DID NOT HAVE THE PROPER COORDINATES ENTERED INTO THE FMS NAVIGATOR. A 'GROSS NAVIGATIONAL ERROR' RPT WAS FILED BY GANDER CTR. CONTRIBUTING FACTORS INCLUDED THE FOLLOWING: THE PF AND ACTING AS PIC WAS THE OWNER OF THE ACFT. OUR COMPANY OFFERS A PLT ASSISTANCE PROGRAM TO HELP NEW OWNERS BECOME FAMILIARIZED WITH THE REAL-WORLD FLYING CHARACTERISTICS AND OP OF THEIR SINGLE-PLT; SWEPT-WING PREMIER 1'S. NORMALLY; OUR COMPANY REQUIRES 2 PLTS; WHO ARE TRAINED IN INTL PROCS TO BE ON BOARD ALL INTL FLTS. THIS HELPS DEFEAT THE LANGUAGE BARRIERS THAT OFTEN EXIST AND ALSO ENSURES THAT THERE IS SOMEONE KNOWLEDGEABLE BACKING UP THE OTHER PLT WHEN CLRNCS ARE COPIED AND FLT PLANS ARE ENTERED INTO THE FMS. 1) 'CREW COORD' WAS MINIMAL WITH THE CUSTOMER PIC. THE CUSTOMER DID NOT TRULY TAKE COMMAND OF THE OP -- JUST THE FLYING. 2) WE EXPECTED ONE CLRNC AND RECEIVED ANOTHER. 3) THE FATIGUE OF XING 6 TIME ZONES IN A 24 HR PERIOD WAS BEGINNING TO BUILD. 4) GANDER ACKNOWLEDGE OUR ESTIMATE TO THE INCORRECT FIX WITH NO CORRECTIONS. 5) OUR COLLINS AMS 3000 NAV DISPLAYS LATITUDE/LONGITUDE FIXES ON IT'S CDU AS 'LL01' OR 'LL02;' ETC. INSTEAD OF BY THE ACTUAL LATITUDES AND LONGITUDES. 6) I DID NOT REVERIFY MY OWN ENTRY AFTER I HAD MADE THE CORRECTIONS TO THE LOADED FLT PLAN. 7) WE WERE DEALING WITH A DATA CONCENTRATOR UNIT FAILURE AND ASSOCIATED FAILURES CAUSED BY THE LOSS OF THE DCU SHORTLY AFTER TKOF. 8) THIS WAS THE 4TH TIME I HAD MADE THE XING IN THE LAST YR AND WAS PROBABLY OVERLY COMFORTABLE WITH IT; LETTING MY GUARD DOWN BECAUSE I WASN'T FLYING AND THE WX WAS NICE. 9) THE ACFT WAS NOT RVSM/MNPS AUTH NOR DID IT HAVE A HIGH FREQ RADIO. 10) LANGUAGE BARRIERS. A POSSIBLE IMPROVEMENT TO THE N ATLANTIC NAV SYS WOULD BE TO NAME COMMONLY USED LATITUDE/LONGITUDE FIXES AROUND THE GREENLAND ARPTS; WHICH ARE OFTEN USED AS FUEL STOPS. (THEY HAVE ALREADY DONE THIS ALONG THE CANADIAN COAST AND AROUND ICELAND.)