B737-300 CREW HAD TRACK DEV WHILE FLYING THE SKEBR 2 RNAV APCH INTO LAS.

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WHILE ON THE SKEBR ARR IN TO LAS; WE APCHED MISEN. JUST PRIOR TO MISEN; ZLA GAVE US CLAAR AT 13000 FT AND 250 KTS. MISEN IS PROGRAMMED AT FL240. WE WERE AT FL190 DUE TO TURB CONDITIONS (OUR FINAL ALT). SO THAT WE COULD OBTAIN THE DSCNT PROFILE IN THE FMC IMMEDIATELY PRIOR TO MISEN; WE HIT THE 'DELETE' BUTTON AND KEY 1R TO DELETE THE INPUT ALT AT MISEN AND ENTERED FL190 AND HIT EXECUTE. THIS TOOK MAYBE 5-10 SECONDS TO COMPLETE; BUT IT JUST SO HAPPENED THAT IT TOOK PLACE AS WE PASSED OVER MISEN (STARTED JUST PRIOR AND EXECUTED JUST PAST). FOR SOME REASON; MISEN NEVER DROPPED OUT AS WE PASSED OVER (POSSIBLE SOFTWARE GLITCH). AFTER THE EXECUTE BUTTON WAS PUSHED; WE HAD ACTUALLY PASSED OVER MISEN; BUT SINCE IT DID NOT DROP OUT; THE ACFT STARTED A L TURN. SINCE WE WERE EXPECTING A TURN TO THE N ANYWAY (AT CLAAR); WE DIDN'T REALIZE WHAT THE ACFT WAS DOING WAS NOT RIGHT. MY 1ST INDICATION THAT SOMETHING WAS WRONG WAS MY HSI WAS 180 DEGS OUT WITH THE COURSE LINE FULLY DEFLECTED TO THE L. WE PROBABLY TURNED APPROX 40 DEGS BEFORE WE WERE ABLE TO FIGURE OUT WHAT WAS GOING ON. BEING IMC AND OPERATING ABOUT XA00 BODY CLOCK TIME PROBABLY CONTRIBUTED TO OUR TEMPORARY LOSS OF SITUATIONAL AWARENESS. WHEN WE REALIZED WHAT WAS GOING ON; I SELECTED 'HDG SELECT' AND STARTED A TURN BACK TO CLAAR. LAX CTR ASKED IF WE WERE TURNING. WE RESPONDED 'YES; BACK TO CLAAR.' WE FELT THERE WAS NO PROB WITH LAX CTR AND DID NOT CONSIDER A COMPANY RPT AT THE TIME. AFTER THINKING ABOUT THE POTENTIAL CONSEQUENCES OF THIS HAPPENING POSSIBLY IN A MORE MOUNTAINOUS TERRAIN (ACR IN SOUTH AMERICA); FELT THE NEED TO SUBMIT.