A B737-300 FLT IS NARROWLY MISSED BY ANOTHER ACR ACFT ON ITS TKOF ROTATION ON RWY 25R AT LAS; NV.

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WE FLEW A VISUAL APCH TO RWY 25L LAS. FO WAS FLYING. AFTER UNEVENTFUL LNDG; FO EXITED RWY AT INTXN A6. AS WE WERE EXITING AT INTXN A6; LAS TWR CLRED US TO CROSS RWY 25R AT INTXN A6 AND THEN TO GND. I (CAPT) READ BACK THE CLRNC; TOOK CTL OF THE ACFT AND PROCEEDED TO TAXI ACROSS RWY 25R. FO CLRED US TO THE R. AS OUR ACFT APCHED THE RWY 25R SURFACE (CROSSED ONTO RWY 25R APPROX 10-15 FT) FO SAID THERE WAS AN ACFT COMING TOWARD US AND TO HURRY ACROSS! I LOOKED TO THE R AS I ADDED PWR TO EXPEDITE ACROSS. I OBSERVED AN ACFT ON RWY 25R ABOUT 2000 FT DOWN THE RWY. THE ACFT HAD JUST ROTATED AND WAS APPROX 10-20 FT IN THE AIR. I CONTINUED TO EXPEDITE ACROSS RWY 25R AND THEN I CONTACTED TWR. I ASKED THEM WHAT HAD HAPPENED; AND TOLD THEM THAT THEY CLRED US ACROSS THE RWY AS ANOTHER ACFT WAS ON ITS TKOF ROLL. THE TWR AGREED. I TAXIED TO THE GATE AND SHUT DOWN. IN OPS; I TALKED TO THE LAS TWR SUPVR. HE SAID THAT INDEED IT WAS THEIR MISTAKE AND APOLOGIZED. HE SAID THEY WOULD BE REVIEWING THE TAPES/RECORDINGS AND WOULD BE GOING THROUGH THEIR PROCS. I CALLED OUR DISPATCH AND OPS DUTY MGR AT OUR HEADQUARTERS. HE MADE THE APPROPRIATE CALLS TO OTHER DEPTS. HE THEN CALLED BACK TO LAS AND INFORMED ME THAT IT WAS OK TO CONTINUE IF WE FELT OK TO CONTINUE. WE SUBSEQUENTLY FLEW 2 MORE LEGS TO FINISH THE TRIP. THIS RWY INCURSION OCCURRED DUE TO CTLR ERROR. THE SUN WAS SETTING IN THE W AT THE TIME OF THE INCIDENT. THE FO WAS NOT ABLE TO PICK UP ACFT Y'S MOTION UNTIL WE HAD TAXIED ONTO RWY 25R. HE THOUGHT THE ACFT WAS IN POS AND HOLD. THIS MAY HAVE BEEN DUE TO THE DISTANCE/SUN ANGLE. I'VE BEEN SEARCHING FOR WAYS IN WHICH THIS COULD HAVE BEEN PREVENTED. THE MOTION OF AN ACFT NOSE-ON IS HARD TO PICK UP AT THESE DISTANCES. ATC TWR CTLRS FREQUENTLY TAXI ACFT ACROSS RWYS WITH OTHER ACFT IN POS. THESE ACFT USUALLY HAVE SOME; IF NOT ALL; OF THEIR EXTERIOR LIGHTS ON. FORTUNATELY; THIS INCIDENT DID NOT RESULT IN ANY INJURIES. SUPPLEMENTAL INFO FROM ACN 465682: AS WE APCHED RWY 25R; I CLRED THE RWY. I DID SEE AN ACFT IN THE DISTANCE IN WHAT APPEARED TO BE IN TKOF POS; BUT SAW NO MOVEMENT. AS WE CROSSED THE FIRST 1/4 OF THE RWY; I NOTICED SLOW MOVEMENT OF THE ACFT. FOR A SPLIT SECOND; I THOUGHT THAT MAYBE THE ACFT HAD JUST LANDED; AND WAS GOING TO TURN OFF AT THE NEXT TXWY. AT ABOUT 1/2 WAY ACROSS THE RWY; I NOTICED THE NOSE ROTATE; AND I TOLD THE CAPT TO HURRY ACROSS. THE TKOF ACFT PASSED BEHIND US AND ABOUT 200-300 FT IN THE AIR. POSSIBLE SOLUTION: DEVISE SOME WAY TO TELL IF AN ACFT IS IN POS AND HOLD; TAKING OFF; OR LNDG ROLLOUT -- IE; FLASHING LIGHTS; COLORED LIGHTS; ETC.