B737-300 CREW HAD A TRACK DEV DEPARTING LAS ON AN RNAV DEP.

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LNAV DEP ON THE BAOCH 1 OUT OF LAS. ALL SWITCHES SET CORRECTLY FOR TKOF AND RWY UPDATE ACCOMPLISHED. CDI WAS CTRED ON TKOF ROLL. FO WAS PF. AT ABOUT 1000 FT AGL WITH THE LNAV ENGAGED; THE FO SELECTED AUTOPLT AND ACFT TURNED L ALTHOUGH THE FIRST POINT; REBELL; I BELIEVE; WAS SUPPOSED TO BE ON THE NOSE. WITH BOTH SWITCHES IN NAV; THERE WAS NO WAY TO BACK UP THE LNAV. THE AUTOPLT WAS DISENGAGED AND WE CONTINUED ON A HDG OF ABOUT 230 DEGS. I SELECTED DIRECT TO THE FIX ON THE CDU AND IT WAS STILL COMMANDING TO TURN FURTHER L. I THEN NOTICED THE REQUIRED NAV PERFORMANCE WAS 1.0 AND THE ACTUAL NAV PERFORMANCE WAS 5.65. BY THIS TIME; WE WERE HEADING IN A SW DIRECTION AND I INFORMED ATC OUR LNAV WAS OUT OF LIMITS AND WE NEEDED VECTORS. WE WERE ASSIGNED A HDG AND THE MCCARRAN DEP TO HEC. ABOUT 30 SECONDS LATER THE UNABLE REQUIRED NAV PERFORMANCE MESSAGE APPEARED ON THE CDU. WITHIN 2 MINS OR SO; THE ACTUAL NAV PERFORMANCE CAME BACK DOWN TO LESS THAN 1 NM; WELL WITHIN LIMITS. ATC INQUIRED AS TO WHAT HAPPENED ON THE INITIAL TURN AND I TOLD THEM WE HAD A SUDDEN PROB WITH THE LNAV ON THE DEP. THERE WERE NO TFC CONFLICTS. WE CONTINUED THE REMAINDER OF THE DAY AND HAD NO FURTHER PROBS WITH THE LNAV SYS. MAINT WAS INFORMED OF THE PROB WHEN WE LANDED AT THE END OF THE DAY. WE CONCLUDED IT WAS PROBABLY A HICCUP WITH THE LNAV COMPUTER. I ASKED THE FO IF HE WAS SURE HE DID THE RWY UPDATE AND HE ASSURED ME THAT HE DID. I WOULD LIKE TO NOTE IT WAS PROBABLY 2 MINS BEFORE THE MESSAGE ON THE CDU SAID THE ACTUAL NAV PERFORMANCE WAS OUT OF LIMITS. WE WERE VMC; SO IT WASN'T A REAL PROB; BUT IF WE HAD BEEN IN THE WX; WITH NO BACKUP TO THE LNAV DEP; IT COULD HAVE BEEN A BIT MORE DISCONCERTING. IT TOOK A WHILE TO FIGURE OUT EXACTLY WHAT THE PROB WAS AS IT IS NOT NORMAL TO LOOK AT THE BOTTOM OF THE LEGS PAGE TO CHK THE ACTUAL NAV PERFORMANCE AND REQUIRED NAV PERFORMANCE.