AN MD80 FLT CREW RECEIVED WRONG CLRNC THAT THE CTLR DIDN'T CATCH IN THE READBACK; RESULTING IN THE ACFT TURNING IN THE WRONG DIRECTION ON DEP.

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FO CONTACTED CLRNC AND RECEIVED WHAT WAS A LITTLE DIFFERENT DEP FOR THIS ARPT. WE WERE GIVEN RWY HDG TO 11 DME; THEN R TURN TO INTERCEPT THE 145 DEG RADIAL OFF THE VOR; AND A CLB TO A LOWER ALT THAN NORMAL (6000 FT). THE FO REPEATED THE CLRNC SINCE IT WAS NOT OUR FILED AND DID NOT INCLUDE THE NORMAL SID FOR THIS ARPT. AFTER TKOF; WE FLEW THE CLRNC; AS COPIED; AND WHEN WE CONTACTED DEP THEY SEEMED A LITTLE SURPRISED WE WERE TURNING R. DEP DID SEEM TO HAVE RADAR PROBS AS THEY HAD US IDENT TWICE AND WERE ASKING FOR ALTS. THERE INITIALLY WAS A PROB GETTING A CLRNC BECAUSE THE #1 RADIO ANTENNA WAS APPARENTLY BEING BLOCKED BY THE ACFT FUSELAGE. WE SWITCHED TO THE #2 RADIO AND EVERYTHING WORKED FINE THEN. BOTH PLTS LISTENED TO THE CLRNC AS IS COMPANY POLICY. IT SEEMS TO ME IF WE COPIED THE TURN WRONG; THE CLRNC CTLR SHOULD HAVE CORRECTED US WHEN WE READ IT BACK TO HER. SECONDLY IT SEEMS IF WE STARTED A TURN IN THE WRONG DIRECTION; THE DEP CTLR SHOULD HAVE TURNED US IN THE CORRECT DIRECTION. SINCE THIS WAS NOT A NORMAL DEP FROM THIS ARPT; THE TURN TO INTERCEPT THE RADIAL SHOULD HAVE BEEN TO A SPECIFIC HDG WHICH WOULD HAVE AVOIDED THE POSSIBILITY OF ANY MISTAKES.