ON TAXI OUT; B737 FMC ANNUNCIATED MESSAGE 'VERIFY POS.' FO AND CAPT DETERMINED POS WAS CORRECT. ENRTE SEA HAD SERIES OF FMC MESSAGES REGARDING POS. ELECTED TO CONTINUE FLT USING RAW DATA. COMPANY ADVISED OF PROB AND CONTINUED TO SEA. REFUSED DIRECT CLRNC ENRTE ACCOUNT PROB.

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ON TAXI OUT FROM SFO THE FMC ANNUNCIATED THE MESSAGE 'VERIFY POS.' BOTH THE FO AND MYSELF CONFIRMED THAT THE DATA LOADED INTO THE FMC WAS CORRECT. IT WAS. FO CONFIRMED THAT FMC SHOWED US WITHIN .2 NM OF OUR POS. WE ALSO DISCUSSED THAT SHOULD AN ERROR DEVELOP WITHIN THE FMC WE COULD CONTINUE RAW DATA. TKOF AND DEP WAS NORMAL. HOWEVER; ON CLBOUT; WE BEGAN TO GET THE FOLLOWING SERIES OF MESSAGES: 'VERIFY POS;' 'IRS NAV ONLY;' AND 'IRS (L).' AN FMC/DME CHK ON RBL SHOWED A DIFFERENCE OF 3 DME (2 IS THE LIMIT). ABOUT THIS SAME TIME CTR OFFERED US A DIRECT CLRNC. WE DECLINED STATING THAT WE WERE HAVING TROUBLE WITH OUR RNAV AND THAT WE WOULD BE FLYING OUR FILED RTE RAW DATA. WE SENT THE APPROPRIATE MESSAGES TO LINE MAINT AND DISPATCH. WHEN WE WERE HANDED OVER TO ZSE WE WERE AGAIN OFFERED DIRECT; AND AGAIN WE DECLINED STATING OUR PROB. HE GAVE US RADAR VECTORS TO SEA. IN OPS AFTER THE TRIP I FILED THE REQUIRED CAPT'S RPT. THE ENTIRE TRIP PROCEEDED WITHOUT INCIDENT OR TROUBLE USING RAW DATA DISPLAYS AS OPPOSED TO THE FMC/MAP FUNCTIONS. IT WAS NOTED THAT THE FMC WAS OFF 20 NM BY BTG BUT DID NOT DEGRADE ANY FURTHER; AND THIS WAS NOT A FACTOR IN THE MODE (VOR) USED. HINDSIGHT BEING 20/20; I PROBABLY SHOULD HAVE STOPPED THE ACFT DURING TAXI OUT AND REALIGNED THE IRS'S. IF THIS WAS NOT POSSIBLE; A DEFERRAL SHOULD HAVE PROBABLY BEEN OBTAINED. THIS REALLY DIDN'T CROSS MY MIND AT THE TIME AS THE DATA ALL SEEMED OK AND WE DID AN UPDATE AT THE RWY. HOWEVER; IN THE REMOTE POSSIBILITY THAT THIS HAPPENS AGAIN THAT WOULD BE MY COURSE OF ACTION.