FLT CREW OF B737-500 OVERSHOT CLRED ALT WHEN COCKPIT DISCIPLINE BROKE DOWN REGARDING VERIFICATION OF CLRED ALT IN THE ALT ALERT WINDOW.

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CLBING TO FL280 ON THE CHILY 1 DEP OUT OF PHX; LNAV ENGAGED; I WAS FLYING. PRIOR TO REACHING CRUISE ALT; CTR GAVE US A L TURN TO A HDG OF 310 DEGS TO INTERCEPT THE AIRWAY W OF DRK. FO MISSED THE RADIO CALL; BUT I READ IT BACK VERBATIM. FO THEM ASKED WHAT ATC HAD SAID; AND I REPEATED IT BACK TO HIM. I SELECTED HDG ON THE MCP AND VOR LOC; TURNED TO 310 DEGS; SWITCHED OUT OF NAV AND SET UP THE OUTBOUND COURSE AND VERIFIED DRK WAS IN THE NAV COM. THE FO VERIFIED THIS WITH ME. THEN ATC ASKED US TO VERIFY LEVELING AT FL280. I LOOKED AT THE ALT ALERTER AND SAW THAT FL310 WAS SET. I RESPONDED TO ATC NEGATIVE; CLBING TO 310 DEGS ASSIGNED. THEN IT DAWNED ON ME THAT WE WERE ONLY ASSIGNED FL280; WE WERE CURRENTLY AT FL288. I QUICKLY CORRECTED BACK TO FL280. ATC ACTUALLY APOLOGIZED TO US; STATING THAT WE MUST HAVE MISUNDERSTOOD HIS HDG OF 310 DEGS FOR FL310. OF COURSE; THIS WAS NOT THE CASE. I QUESTIONED THE FO ON HOW THE ALT ALERTER HAD INADVERTENTLY BEEN CHANGED. HE SAID THAT HE MISUNDERSTOOD ME WHEN I REPEATED THE ORIGINAL RADIO CALL TO HIM THAT HE HAD MISSED. I STATED TO HIM THE IMPORTANCE OF VERIFYING WITH THE OTHER PLT ANY TIME THE ALT IS CHANGED IN THE ALT ALERTER. I NEVER SAW HIM CHANGE THE ALT. HE APOLOGIZED; AND UNDERSTOOD HIS MISTAKE. WHILE ALL OF THIS WAS GOING ON; THE VOR LOC CAPTURED AND STARTED TO TURN OUTBOUND ON THE RADIAL. I NOTICED THAT IT HAD ENGAGED TOO EARLY; AND NEVER INTERCEPTED THE RADIAL. I STARTED TO CORRECT BACK TO THE RADIAL; BUT ATC NOTICED THE DEV AND GAVE US A HDG TO CORRECT BACK; AND THEN A FURTHER HDG TO THE N TO KEEP US OUT OF RESTR AIRSPACE. WE EVENTUALLY WERE GIVEN DIRECT EED AND ON COURSE; AND SHORTLY THEREAFTER SWITCHED TO THE NEXT CTLR. IN HINDSIGHT; I NEED TO PAY MORE ATTN TO THE LAST ALT ASSIGNED AND MY LEVELOFFS; AND NOT NECESSARILY THE ALT IN THE ALERTER. BECAUSE I WAS DISTR FROM THE ALTDEV; I DID NOT RESPOND QUICKLY ENOUGH TO THE UPCOMING COURSE DEV. SIMPLY PUT; FLY THE AIRPLANE; DON'T LET IT FLY YOU! SUPPLEMENTAL INFO FROM ACN 592108: AS WE PASSED THROUGH FL260; I (AS THE PNF FO) WAS MAKING A LOGBOOK ENTRY FOR OUR DEP TIME.