AN MDT TAKES OFF FROM DCA WITH COMPASS NOT SET TO CORRECT HEADING. ACFT DOES NOT FOLLOW HEADINGS GIVEN BY TRACON AND THE ACFT COMES CLOSE TO ENTERING THE PROHIBITED AREA N OF DCA.

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DURING TAXI TO ASSIGNED RWY 36; WAS IN THE PROCESS OF DOING CHKLIST. NOTICED ANOTHER ACFT AND FOCUSED ON HIM LEADING ME TO MISS MY TXWY TO RWY 36 WITH INSTRUCTION TO HOLD SHORT OF RWY 3. GND CTL ADVISED US THEN TO HOLD SHORT OF RWY 3 ON THE TXWY I WAS ON. DURING THIS TIME I HAD BEGUN TO SLAVE MY COMPASS TO THE PROPER HEADING; BUT WAS INTERRUPTED WHEN GND CTL CALLED. WE WERE CLRED TO TKOF ON RWY 36 AND OUR CLRNC WAS TO TURN L TO 330 DEGS. RIGHT AFTER TKOF I OBSERVED MY COMPASS HEADING READING 270 DEGS. I ASKED THE FO TO TRY AND VERIFY COMPASS HEADINGS; AS MY COMPASS SHOULD HAVE BEEN 360 DEGS. IN THE TIME IT TOOK TO SORT OUT THE COMPASS PROB; WE WERE INSTRUCTED BY ATC TO MAKE IMMEDIATE L TURN TO 300 DEGS TO AVOID RESTR AREA. WE DID TURN IMMEDIATELY TO THE L AT THE SAME TIME TRYING TO SLAVE THE COMPASS TO THE PROPER HEADING. ATC ASK US TO CALL WHEN WE ARRIVED AT OUR DEST. I CALLED; BUT THE PERSON ASKING FOR THE CALL WAS NOT AVAILABLE. I LEFT MY NAME; PHONE NUMBER AND AS OF THE CURRENT TIME XX20 LCL TIME; HAVE NOT HAD ANY RESPONSE. I FEEL THAT INTERRUPTION OF THE CHKLIST CONTRIBUTED TO THE COMPASS NOT BEING PROPERLY SET. GREATER ATTN TO CHKLIST DISTR WITH A CHKLIST FOLLOW UP TO INSURE ALL CHKLIST ITEMS ARE COMPLETED. SUPPLEMENTAL INFO FROM ACN 383830: CAPT'S COMPASS WAS NOT SET OR ALIGNED ON THE GND. TAXI INSTRUCTIONS WERE GIVEN. ACFT DEPARTS AND IS FLOWN ON RWY HEADING OFF RWY 36 FOR SECONDS. TWR INSTRUCTS TO MAKE AN IMMEDIATE L TURN TO 300 DEG HDG TO AVOID PROHIBITED AREA N OF DCA. CAPT COMPLIES. CAPT REQUESTED A VERIFICATION OF HEADING WHILE ON THE TURN. VERIFICATION OF COMPASS HEADING TOOK A COUPLE OF SECONDS AFTER CAPT'S REQUEST DUE TO THE FACT THAT THE ACFT WAS ALREADY IN A TURN TO 300 DEGS (45 DEG BANK ANGLE) AS REQUESTED BY ATC.