FLC OF A B737-800 TRANSPOSES ATC CLRNC AND INITIATES WRONG POINT CLB.

Narrative

ENRTE TO SJU FROM EWR (RTE A300 NON RADAR) AT FL330; COMMERCIAL RADIO RELAYED A MESSAGE FROM ZNY TO CLB TO FL370. COMMERCIAL RADIO TOLD US TO START A CLB TO FL370 AT 3030N; TO CROSS PULLS INTXN AT FL370. I READ BACK AND WROTE DOWN 33N TO START THE CLB. THE CTLR CORRECTED ME AND TOLD ME TO CLB AT 3030N. I WROTE DOWN 30N; UNDER THE 33N; AND CONFUSED THIS FOR 333 ON WHICH THE CAPT HAD ALSO WRITTEN DOWN. WE THEN PROCEEDED TO CLB AT 3330N AND RPTED AT FL370. WE WERE THEN TOLD BY COMMERCIAL RADIO TO DSND BACK DOWN TO FL330. I THINK THE MAIN THING I COULD HAVE DONE IS TO HAVE REQUESTED THE CLRNC AGAIN; WRITTEN IT DOWN ON A FRESH PIECE OF PAPER; AND THEN CONFIRMED IT WITH COMMERCIAL RADIO AND THE CAPT. SUPPLEMENTAL INFO FROM ACN 480472: AT ABOUT ABEAM BERMUDA 3130N WE WERE SELCALED AND TOLD TO DSND TO FL330 AND TO CALL ZNY ASAP AND WERE GIVEN A PHONE NUMBER. ON THE GND AT SJU; I CALLED ZNY AND WAS TOLD WE HAD A LOSS OF SEPARATION WITH ANOTHER ACFT (REQUIRED SEPARATION WAS 15 MINS; THEY HAD ESTIMATED THAT WE HAD 5 MINS). I BELIEVE ZNY SHOULD HAVE NOT ISSUED THE CLB CLRNC SO FAR IN ADVANCE; +/-300 MI. I NEED TO BE CAREFUL WHEN RECEIVING A CLRNC; ESPECIALLY WHEN SO MANY NUMBERS ARE THE SAME. I ALSO NEED TO BE SURE I UNDERSTAND THE CLRNC; AND STATE IT TO THE OTHER CREW MEMBERS.