FLC OF A DASSAULT FALCON 20 (DA20); DEVIATED FROM THEIR ASSIGNED HEADING AND EXCEEDED AIRSPD BELOW 10000 FT DURING A SID DEP CLB CAUSED BY THE FLC'S CONFUSION OF THE ACFT'S INDICATED HEADING.

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I WAS (AM) A 'LOW MINIMUMS' CAPT; FLYING THE LAST LEG OF MY FIRST TRIP. AFTER GEAR RETRACTION; I XFERRED CTL OF THE ACFT TO MY FO; TO CONTINUE THE 'GATEWAY 3 DEP' OUT OF STL. I ASKED HIM WHERE HE WAS HEADED SINCE HE FLEW THROUGH OUR ASSIGNED HEADING. HE SAID HE WAS TURNING TO (XXX DEGS); WHICH WAS CORRECT; BUT I NOTICED THAT OUR DIRECTIONAL GYROSCOPES WERE OFF BY MORE THAN 40 DEGS. HE REACHED FOR THE KNOB ON HIS RMI AND TURNED IT; HOPING TO MATCH THE DIRECTIONAL GYROSCOPES. BUT IT SPUN MY DIRECTIONAL GYROSCOPE (OUR ACFT ARE NOT STANDARDIZED WITH EQUIP). I DIDN'T KNOW WHAT WAS INDICATING CORRECTLY (IF ANYTHING) SO I TURNED OFF OUR WINDSHIELD HEAT (WHICH THROWS OFF THE COMPASS) TO CHK OUR HEADING AND TO RESET OUR GYROSCOPES. AT THIS TIME; MY FO REACHED DOWN AND TURNED MY COURSE SELECTOR (IN AN ATTEMPT TO FIX THINGS) WHICH COMPOUNDED OUR SIT. I CHOSE TO TAKE CTL OF THE ACFT; SINCE HE WAS BUSY TURNING KNOBS. DEP ASKED ME (US) WHAT SPD WE WERE GOING TO MAINTAIN TO ALT. AS I KEYED THE MIKE (MINE WAS THE ONLY SIDE THAT WORKED; AGAIN COMPOUNDING AN UNDESIRABLE SIT) TO SAY 270 KTS; I GLANCED DOWN AT MY AIRSPD INDICATOR; WHICH INDICATED 305 KTS. AS I SAID '270 KTS;' I PULLED THE PWR LEVERS TO IDLE; EXTENDED THE AIRBRAKES AND PULLED THE NOSE UP. I DON'T KNOW HOW LONG I WAS ABOVE 250 KTS. I REMEMBER CONFIRMING MY DIRECTIONAL GYROSCOPE WITH THE RWY HEADING; BUT DON'T RECALL CHKING MY RMI. WE WERE NOT RUSHED TO TKOF. I WILL ALWAYS CHK BOTH DIRECTIONAL GYROSCOPES AGAINST A KNOWN HEADING. I WILL INSURE THE FO ALSO RESETS THE GYROSCOPES (AS CALLED FOR IN THE CHKLIST) AND VISUALLY DOUBLE CHK IT. I WILL DELEGATE DUTIES RESPONSIBLY (HIS LEG; LET HIM FLY; I WILL WORK THE PROB). ONE PERSON NEEDS TO STAY WITH THE ACFT AND FLY IT PROPERLY. IF I HAVE ANY KIND OF PROB (THAT MAY TAKE US OFF COURSE/AIRSPD; ETC); I WILL NOTIFY ATC; AND ASK FOR INFO AND ASSISTANCE. IN THIS CASE; I SHOULD HAVE INFORMED ATC OF A GYROSCOPE ABNORMALITY; ASKED FOR OUR TRACK; INFORMED THEM WE MAY BE OFF COURSE (ASSIGNED HEADING) FOR A BRIEF TIME WHILE WE RESET OUR GYROSCOPES. WHEN I DO ENCOUNTER A PROB AGAIN; I WON'T RUSH TO FIX IT. I WILL STOP; CONSIDER THE PROB; CONSIDER WHAT STILL WORKS; THEN WORK THE SOLUTION.