TRACK DEV ON DEP FROM SMO; CA. CLRNC COPIED WAS NOT CORRECT.

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RECEIVED IFR CLRNC FROM SMO GND CTL SHORTLY BEFORE XA00 AM. WROTE DOWN AND READ BACK AS FOLLOWS ;CLRED TO RNO VIA RWY HEADING TILL INTERCEPTING LAX 310 DEG RADIAL; THEN R TURN TO 350 DEGS; VECTORS TO INTERCEPT V23; SHAFTER; AS FILED; CLB AND MAINTAIN 3000 FT; EXPECT FL330 IN 5 MINS. DEP FREQ 125.2; SQUAWK XXXX.' WE DEPARTED AT APPROX XA05 AM AND UPON INTERCEPTING THE LAX 310 DEG RADIAL; TURNED TO HEADING 350 DEGS AT 3000 FT MSL. AS WE TURNED; WE WERE HANDED OFF TO DEP AND THEY SHORTLY THEREAFTER ASKED US TO SAY OUR HEADING. WE RESPONDED '350 DEGS' AND WERE TOLD WE WERE SUPPOSED TO BE ON HEADING 250 DEGS. WE THEN TURNED TO CORRECT HEADING OF 250 DEGS. THIS DEV WAS; I BELIEVE; DUE TO MY HAVING COPIED 250 DEGS AS 350 DEGS WHEN RECEIVING MY CLRNC AND THE CTLR NOT CORRECTING IT WHEN I READ IT BACK AS 350 DEGS. WHEN I CHKED IT ON THE CHART; IT LOOKED REASONABLE TO INTERCEPT V23 ON A 350 DEG HDG. IT SEEMS TO ME THAT ALL PROCS WERE CORRECTLY FOLLOWED BY ALL PARTIES INVOLVED IN THE CLRNC DELIVERY PROCESS; BUT DUE TO EITHER UNDETECTED RADIO INTERFERENCE OR JUST 'MISHEARING;' ERRORS CREPT IN.