CPR X HAD LTSS FROM SMT Y. SYS ERROR.

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CPR X ON A 7 MI FINAL FOR RWY 36 AT DCA AND WERE TOLD BY APCH CTL TO SLOW TO 170 KTS FOR SPACING WITH AN LGT ON R BASE; TURNING FINAL. WE DID SO; AND WERE SWITCHED TO TWR AND SUBSEQUENTLY CLRED TO LAND RWY 36. TSTMS HAD PASSED THROUGH THE AREA AND ALL ARPT SURFACES WERE WET. DURING ROLLOUT; WE WERE TOLD BY LCL CTL IN AN EMPHATIC TONE; TURN L NEXT TAXIWAY AND DON'T MISS IT! WHILE INITIATING THE TURN; THE PLT IN THE R SEAT COMMENTED TO ME 'LOOK AT THIS.' IT WAS SMT Y THAT WAS ALSO CLRED TO LAND ON RWY 33; ROLLING THROUGH THE INTXN OF RWY 36; OUR RWY. TFC WAS NOT POINTED OUT TO EITHER ACFT; NOR WAS EITHER ASKED TO HOLD SHORT OF; OR ROLL THROUGH THE XING RWY. RWY 36 TO THE INTXN OF RWY 33 IS ABOUT 5000 FT. RWY 33 TO THE INTXN OF RWY 36 IS ABOUT 2600 FT. WE TURNED ONTO TAXIWAY 'I' WHICH IS IMMEDIATELY S OF RWY 33. HAD WE NOT BEEN ABLE TO TURN ONTO TAXIWAY 'I'; I FEEL VERY STRONGLY THAT A COLLISION WOULD HAVE OCCURRED. I HAVE BEEN A CTLR FOR OVER 5 YRS; AND WHAT BOTHERS ME THE MOST IS THAT THE LCL CTLR JUST CONTINUED TO WATCH A VERY DANGEROUS SITUATION DEVELOP WITHOUT ATTEMPTING TO TAKE ANY CORRECTIVE ACTION.