B737-500 CREW HAD A TRACK AND ALTDEV DEPARTING LAS ON A RNAV DEP. THE ACFT OVERTURNED TOWARD THE FIX CLRED TO.

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WE WERE DEPARTING OFF OF RWY 1R AT LAS. OUR CLRNC WAS HEADING 050 DEGS CLB TO 7000 FT; EXPECT VECTORS FOR THE COWBY RNAV DEP. ALL APPROPRIATE PREFLT PROCS WERE ACCOMPLISHED USING EXTRA CAUTION DUE TO THE PROBS DISCUSSED IN THE RECENT FLT BULLETIN. AFTER TKOF; WE WERE GIVEN FURTHER CLRNC TO CLB TO FL190; PROCEED DIRECT TO NAPSE AND COMPLY WITH RESTRS. WE BOTH CONFIRMED 7000 FT IN THE ALT WINDOW AND NAPSE WAS INPUT IN THE LNAV AND EXECUTED. INITIALLY; THE ACFT BEGAN A TURN TO THE R WHICH WAS AS EXPECTED. ABOUT THIS TIME; LAS DEP CALLED OUT TFC AND BOTH OF US BEGAN TO CLR OUTSIDE. WHEN I CAME BACK IN TO CHK THE INSTS; THE ACFT HAD TURNED PAST THE COURSE BY ABOUT 30-40 DEGS. THERE WAS THE TYPICAL RESPONSE OF WHERE IS THIS THING TAKING US WHEN I NOTICED WE WERE ALSO CLBING AT A PRETTY GOOD CLIP AND APCHING THE LEAD POINT FOR LEVELOFF AT 7000 FT. I DECIDED TO DISENGAGE THE AUTOPLT AND MANUALLY LEVELOFF AND TURN BACK TOWARD NAPSE WHEN THE TCASII EMITTED AN RA (REDUCE CLB). SINCE I WAS ALREADY LEVELING OFF; I CONTINUED. I OVERSHOT 7000 FT BY ABOUT 200 FT AND IMMEDIATELY DSNDED BACK TO 7000 FT. BOTH OF US THOUGHT THE AUTOPLT HAD GONE HAYWIRE BUT HONESTLY; AFTER SOME REFLECTION; I DON'T REMEMBER ENGAGING IT. NORMALLY; WE SELECT LNAV AT 400 FT AND ENGAGE THE AUTOPLT AT 1000 FT. WE WERE ON A VECTOR THIS TIME AND NOT ON THE LNAV DEP SO LNAV WASN'T SELECTED AT 400 FT AND ALTHOUGH I REMEMBER THINKING ABOUT ENGAGING IT AT 1000 FT; I DON'T THINK I DID BECAUSE: 1) THE AUTOPLT DID NOT TAKE US WHERE THE FLT DIRECTOR WAS DIRECTING US TO GO. 2) I DON'T BELIEVE 7000 FT WAS EVER ACQUIRED. 3) ALTHOUGH A LOT WAS GOING ON IN THE COCKPIT WITH THE TCASII RA; I DON'T RECALL A HORN WHEN I HIT THE DISENGAGE SWITCH ON THE YOKE. I GUESS ALL THAT TIME IN THE -200 COMBINED WITH THE INFO IN THE RECENT FLT BULLETIN PROBABLY KEPT US OUT OF TROUBLE. I THINK PERHAPS THE MOVING MAP DISPLAY WOULD HAVE HELPED; BUT WITH THE TFC CALL DISTRACTING US I CAN'T SAY THAT FOR CERTAIN EITHER. IT'S AN OLD LESSON; BUT WHEN ALL ELSE FAILS; FLYING THE ACFT IS ALWAYS A GOOD IDEA. SUPPLEMENTAL INFO FROM ACN 602015: AS FOR LESSONS LEARNED; WE MUST DILIGENTLY MONITOR THE COURSES DISPLAYED ON THE LEGS PAGE IN CASE THE AUTOPLT STARTS TO WANDER. BOTH PLTS MUST VERIFY A COMMAND BEFORE IT IS EXECUTED. ALTHOUGH WE DID THIS; IT'S POSSIBLE THAT I SIMPLY SAW WHAT I WANTED TO SEE. IN THIS WORLD OF INCREASING AUTOMATION; WE MUST BE READY TO FLY THE AIRPLANE IF THE AUTOPLT WILL NOT.