A B737-300 CREW HAD TRACK DEV IN ZAB CLASS A AIRSPACE.

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THIS CREW FLEW TOGETHER FOR 5 LEGS IN SAME ACFT. ON LEG 3 (PHX-LAX); THE FMC CREATED A RTE DISCONTINUITY AT TEJAY INTXN WHILE FLYING THE PDZ ARR INTO LAX. THIS WAS CAUGHT BY THE CREW AIRBORNE IN CRUISE. THE RTE AS PROGRAMMED LOOKED GOOD ON DECK. LEG 5 WAS THE EXACT SAME RTE AS 3 -- THIS TIME THE FMC CREATED A RTE DISCONTINUITY AT BUCKEYE ON THE SID OUT OF PHX. IT OCCURRED JUST AFTER LEVELOFF AT NIGHT/IMC. HAVING ALREADY GOT A PROB WITH THE FMC; THIS CREW VERIFIED THE RTE PRIOR TO DEP AND IT WAS OK -- NO DISCONTINUITIES. HOWEVER; ONCE AT BUCKEYE; WE FLEW A HDG OF APPROX 260 DEGS FLYING THE J4 AS DEPICTED ON THE SID. WE WERE QUERIED BY CTR AS TO OUR INTENTIONS; AND GIVEN A HDG OF 290 DEGS TO JOIN J4. AT THIS TIME WE NOTICED THE DISCONTINUITY. SEVERAL LESSONS FOR ME AS PLT AND CREW: 1) I ATTRIBUTED THE FMC ERRORS TO PROGRAMMING BY ME. NEW TO ACFT. I BELIEVE THERE WAS SOMETHING WRONG WITH THE FMC. WE WROTE IT UP AT LAX. HOWEVER; ONCE THE CAPT GAVE THE RTE THE OK; I WAS NOT CHKING THE FMC CONSISTENTLY ON DEP; THUS WAS CAUGHT UNAWARE. I HAD A DIFFERENT PAGE ON THE FMC ITSELF; DEPICTING WINDS ALOFT AND TIMES TO VARIOUS POINTS ENRTE. 2) I SHOULD HAVE NOTICED THE INCORRECT HDG OUT OF BUCKEYE. THE ERROR WAS APPROX 30 DEGS OFF COURSE; AND I DID NOT NOTICE THE DEV TILL CTR SAID SOMETHING. 3) AS THE PF; I ASSUMED THE CAPT WOULD TAKE CARE OF EVERYTHING ELSE. I DIDN'T/FAILED TO BACK HIM UP -- POOR CREW COORD. THIS REALLY BOILS DOWN TO TRAINING/CREW COORD. WE BLINDLY FOLLOWED 'THE YELLOW BRICK ROAD.' HAD CTR NOT SAID SOMETHING RIGHT AFTER BUCKEYE; I DON'T KNOW HOW FAR WE WOULD HAVE FLOWN -- PROBABLY TILL WE HIT THE R2306/08 OR R2507. THANK GOODNESS CTR HAD DEMONSTRATED SOME GOOD CREW COORD SKILLS.