UNAUTHORIZED RWY XING BY ACR. PLTDEV.

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I HAD JUST LANDED ON RWY 36L AT DFW. I MANEUVERED THE ACFT OFF THE RWY AT HIGH SPD 2N AT A SPD OF APPROX 40 KTS. THE CAPT THEN TOOK CTL OF THE ACFT AND TAXIED ACROSS TAXIWAY ECHO ONTO TAXIWAY 23 BEHIND ACR Z. AS WE CROSSED TAXIWAY ECHO; WE RECEIVED A CLRNC FROM TWR. BOTH THE CAPT AND I MISUNDERSTOOD THE CLRNC AND BELIEVED IT TO BE TO FOLLOW ACR Z (WHO HAD BEEN CLRED TO CROSS RWY 36R) AND TAXI N ON THE INNER TAXIWAY. AN ACFT Y HAD BEEN CLRED ON TO HOLD ON RWY 36R AND WAS MANEUVERING INTO POS. AS WE WERE HALFWAY ACROSS RWY 36R; TWR CALLED AND TOLD US 'THAT'S NOT WHAT I TOLD YOU TO DO.' WHAT WE HAD BEEN TOLD TO DO WAS TURN L AT TAXIWAY ECHO AND HOLD SHORT OF TAXIWAY 18. CAUSES OF THE ERROR: 1) CREW ANTICIPATING INSTRUCTIONS OF A DIFFERENT NATURE. 2) CREW COORD NOT BEING OPTIMUM AS ACFT CTL HAD JUST BEEN TRANSFERRED. 3) INSTRUCTIONS GIVEN WHEN ACFT WAS ALREADY XING TAXIWAY ECHO. CORRECTIVE ACTIONS: THIS CREW WAS FORTUNATE THAT THERE WAS NO CONFLICT WITH ANOTHER ACFT. AS LONG AS CREWS CONTINUE TO BE HUMAN; ERRORS WILL BE MADE. MANY SOLUTIONS HAVE BEEN PROPOSED TO PREVENT RWY INCURSIONS (I.E.; STOP BARS; LIGHTS; ETC). THIS WRITER CAN'T THINK OF ANYTHING BETTER THAT HASN'T ALREADY BEEN SUGGESTED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: STRUCTURED CALLBACK MADE AS PART OF RWY INCURSION STUDY. CLARIFIED POINT AT WHICH TAXI CLRNC WAS XMITTED AND IT WAS AT SAME TIME THAT TRANSFER OF ACFT CTL WAS TAKING PLACE. NEITHER FLC APPARENTLY HEARD THE TAXI CLRNC CORRECTLY AND WHEN ACR Z WAS CLRED ACROSS 36R THEY FOLLOWED THAT ACFT BECAUSE THAT WAS THE CLRNC THEY EXPECTED. CTLRS VERY BUSY; BUT THINKS INCIDENT COULD HAVE BEEN AVOIDED IF CTLR HAD GIVEN TAXI INSTRUCTIONS SOONER. THEY WERE WATCHING THE ACFT Y MANEUVERING INTO POS ON 36R AND THERE WAS NO CONFLICT WITH THAT ACFT. PIC CALLED DFW TWR LATER TO REVIEW THE INCIDENT WITH ATC SUPVR.