HDG TRACK DEV DURING A NIGHT OP. PUB DEFICIENCY INVOLVED TO A LESSER LEVEL.

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DURING COCKPIT SETUP FOR FLT SFO-DFW I SET UP THE FMS FOR THE FILED DEP WHICH WAS THE SFO6. WHEN CLRNC WAS RECEIVED FROM ATC WE WERE ASSIGNED THE CUIT1 INSTEAD. THIS WAS WRITTEN DOWN BUT WE STILL MISSED THE FACT THAT IT WAS NOT THE SFO6 THAT WAS ALREADY SET UP. WE BRIEFED THE SFO6 AND TOOK OFF WITH THAT IN THE FMS AND STARTED TO FLY THE DEP BY INITIATING A TURN TO 030 DEGS HDG AT 400 FT. TWR ASKED US WHAT SID WE WERE FLYING AND WE SAID THE SFO6. THEY SAID WE WERE SUPPOSED TO BE ON THE CUIT1 AND TO FLY THE CUIT1. I STARTED TO PAGE THROUGH SID PLATES LOOKING FOR THE CUIT1 BUT REALIZED IT WOULD TAKE TOO LONG TO FIND AND READ IT AND I SHOULD BE LOOKING OUTSIDE AT THIS POINT; SO I REQUESTED A HDG AND WAS ASSIGNED 350 DEGS AND TOLD TO CONTACT DEP. DEP ASSIGNED US ANOTHER COUPLE OF TURNS TO CLR TFC BEFORE VECTORING US ON COURSE. AFTER DEPARTING THE TERMINAL AREA; I CHKED THE CLRNC WE COPIED AND VERIFIED THAT WE HAD INDEED BEEN ASSIGNED THE CUIT1. I SEE 2 LESSONS FROM THIS: 1) COMPARE THE WRITTEN CLRNC WITH THE FLT PLAN THAT IS LOADED IN THE FMS. 2) IN THE EVENT AN ACFT DEVIATES FROM THE ASSIGNED DEP; ATC SHOULD GIVE A HDG AND/OR AN ALT INSTEAD OF A NAMED DEP. TKOF IS NOT A GOOD TIME FOR THE CREW TO BE PAGING THROUGH SID PLATES AND IT WILL TAKE VALUABLE TIME TO LOCATE A PLATE AND SET UP NAV FOR IT. THIS TIME COULD CAUSE A LOSS OF SEPARATION. SUPPLEMENTAL INFO FROM ACN 267928: THE SFO6 DEP WAS THE ONE WE EXPECTED AND FILED AND THE CAPT INDICATED IT WAS A PREFERRED DEP FOR OUR FLT. THIS WAS THE FINAL LEG OF A LONG DAY AND THIS SEQUENCE HAD ALWAYS ENDED IN SFO; BUT THIS ADDITIONAL LEG HAD JUST BEEN ADDED. AFTER WAITING 2 HRS FOR THE FREIGHT LOADING TO BE COMPLETE; WE FINISHED OUR CHKLISTS AND RECEIVED OUR CLRNC. I COPIED THE 'QUIET 1' DEP (SID) ALONG WITH THE REST OF OUR CLRNC AND READ IT BACK. THE CAPT ALSO COPIED THE CLRNC. AT THAT MOMENT THE RAMP AGENT PRESENTED THE FINAL PAPERWORK. THAT DISTR MAY HAVE BEEN JUST ENOUGH TO KEEP US FROM BRIEFING THE CLRED SID (QUIET 1). THE SFO6 SID WAS NEVER REPLACED IN THE FMS; OR APPARENTLY IN OUR MINDS EITHER.