WHILE DSNDING ON RADAR VECTOR INTO DFW RWY 35C; AN EMJ CREW WAS CLRED TO 4000 FT BUT OVERSHOT TO 3600 FT.

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DEPARTED FSM; JOINED BYP5 ARR TO DFW. AFTER A HDG VECTOR; ATC ASSIGNED THE WILBR3 ARR. ATC ASSIGNED A 10-15 MIN HOLD AT BIRLE INTXN. AFTER HOLDING; ATC CLRED US TO DFW VIA BYP5 ARR. S OF BYP ATC ADVISED US DFW FLOW WAS CHANGING FROM S TO N AND ASSIGNED RWY 35C. WE ADVISED OF OUR W SIDE PARKING; AND TOLD TO EXPECT RWY 36L. ON DOWNWIND; CLRED FROM 11000 FT TO 4000 FT. BASE LEG WAS A HDG OF 270 DEGS AND AIRSPD OF 180 KTS. FREQ WAS BUSY AND PROMPTED FO ON CONFIRMATION OF RWY ASSIGNMENT. COULD NOT GET A WORD IN. AT 1 DOT TO 1/2 DOT LOC DEFLECTION OF RWY 35C; ATC ASSIGNED HDG OF 350 DEGS TO JOIN. WE QUERIED HIM TO WHICH RWY AND HE ASKED IF WE HAD THE TFC OR ARPT IN SIGHT. WE TOLD HIM WE WERE IMC. AT A POINT; I DON'T RECALL WHEN; A CLRNC FOR ILS RWY 35C WAS GIVEN. AS WE TURNED THROUGH APPROX 330 DEGS; ATC SAID TO TIGHTEN TURN TO 010 DEGS. SIMULTANEOUSLY; TCASII GAVE US A TA TO THE L OF OUR ACFT AND LOOKED TO TRY TO SEE THE TA TFC; BUT WE WERE IMC. I TURNED THE AUTOPLT OFF TO HAND-FLY A STEEP TURN. ATC GAVE US A 040 DEG HDG TO JOIN; AT APPROX 030 DEG HDG WE WERE VISUAL WITH THE ARPT AND I REALIZED I INADVERTENTLY HAD DSNDED TO 3600 FT DURING THE MANEUVER. WHEN INITIATING ALT CORRECTION; ATC CLRED US FOR A VISUAL TO RWY 35C. FO INQUIRED AFTER LNDG IF EVERYTHING WAS OK AND THE CTLR RESPONDED; 'NO PROB.' WE HAD NO REASON TO THINK A LOSS OF SEPARATION HAD OCCURRED. WE COMPLIED WITH ATC INSTRUCTIONS AS BEST AS WE COULD; WHILE THERE SEEMED TO BE SOME CLARITY IN PHRASEOLOGY AND A LATE OR BAD TURN ONTO THE LOC IN THE DFW TERMINAL. SUPPLEMENTAL INFO FROM ACN 622495: I WAS WORKING THE AR3 POS AT D10. ACR Y WAS INBOUND FROM THE NW. I WAS VECTORING THEM FOR A VISUAL APCH TO RWY 36L. ACR X WAS INBOUND FROM THE SE; BEING VECTORED TO A VISUAL APCH TO RWY 35C BY ANOTHER CTLR. I TOLD ACR Y TO TURN TO A 010 DEG HDG TO JOIN THE RWY 36L LOC ABOUT 10 MI SSW OF DFW. THEY WERE DSNDING THROUGH ABOUT 4500 FT. I THEN NOTICED ACR X FLYING THROUGH THE RWY 35C FINAL APCH COURSE. THEY WERE ABOUT 4 MI SE OF ACR Y AND ALSO AT 4000 FT. I HEARD THE OTHER CTLR TELLING ACR X TO TURN R AND JOIN THE RWY 35C FINAL APCH COURSE. I ISSUED TFC TO ACR Y ABOUT ACR X. THE PLT REPLIED WITH 'ROGER.' ACR Y WAS AT 4000 FT AND ACR X WAS AT 3800 FT ABOUT 2 1/2 MI SE OF ACR Y WHEN ACR X CALLED THE ARPT IN SIGHT. VISUAL SEPARATION WAS ACCOMPLISHED; BUT I DON'T KNOW IF IT WAS BEFORE SEPARATION WAS LOST. ACCORDING TO THE OTHER CTLR ACR X WAS INSTRUCTED 2 TIMES BEFORE THEY WENT THROUGH THE LOC; TO TURN R TO JOIN THE RWY 35C LOC. ACR X DIDN'T BEGIN THEIR TURN IN TIME TO JOIN WITHOUT FLYING THROUGH.