SMT X ASSIGNED WRONG HDG HAD LTSS FROM ACR Y. SYS ERROR.

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I WAS TRAINING A CTLR ON LCL CTL POS IN MEM TWR. I HAD BEEN OVER HIS SHOULDER FOR THE PAST HALF HR WATCHING INTENTLY AS HE WAS CLRING SUCCESSIVE DEPS FOR TKOF. WE HAD GOTTEN TO 1 DEP WAITING AT THE RWY. ACR Y GOING TO ORD WITH A RELEASE TIME DUE TO FLOW RESTRICTION. THE FIRST AIRPLANE SMT X TAXIED OUT FROM A FBO AND WENT TO THE RWY BEFORE ACR Y. BECAUSE I HAD BEEN 'HOVERING' OVER THE SHOULDER OF THE TRAINEE; AND WAS ATTEMPTING TO BEGIN TO INSTILL SOME CONFIDENCE TO THE TRAINEE I DID NOT CHK THE DEP GATE OF SMT X WHICH WOULD DETERMINE WHAT HDG SMT X SHOULD GET OFF THE ARPT. THE TRAINEE CLRED SMT X FOR TKOF ON A 210 DEG HDG WHEN THE HDG FOR THE PARTICULAR GATE SHOULD HAVE BEEN 150 DEG. ACR Y WAS CLRED FOR TKOF ABOUT A MIN OR SO LATER ON RWY HDG. THE AIRPLANES WERE INITIALLY SEPARATED. THE DEP CTLR WHO WAS WORKING SMT X FAILED TO RECOGNIZE THE 210 DEG HDG ON SMT X'S FLT PROGRESS STRIP AND TURNED THE ACFT TO A 070 DEG HDG COMPROMISING THE INTEGRITY OF THE INITIAL SEPARATION WITH ACR Y. SMT X WAS TALKING TO THE E DEP CTLR AND ACR Y TO THE W DEP CTLR. SUPPLEMENTAL INFO FROM ACN 202564: I WAS WORKING 6 TO 8 ACFT ON DR-V (DEP E RADAR.) SMT X RPTED AIRBORNE OFF 18L HDG 210. DUE TO THE NEED TO INCREASE SPACING BTWN ACFT E OF THE ARPT. I DID NOT RESPOND TO SMT X FIRST CALL. A SHORT TIME LATER I ISSUED SMT X RADAR CONTACT AND A CLB TO 5000 FT. AFTER A FEW SECONDS; I TURNED SMT X TO A HDG OF 070 DEG. (ACCORDING TO PROC AN ACFT CAN BE TURNED TOWARD HIS RTE LEAVING 2000 FT.) THE TWR CTLR CLRED ACR Y FOR TKOF OFF 18L. ACCORDING TO DARTS THE ACFT WERE 800 FT AND .66 MI APART. I THINK TFC VOLUME ON DEP HAVING TO VECTOR FOR ADDITIONAL SPACING; AND TRAINEE ON THE LCL CTL POS WERE CONTRIBUTING FACTORS.