A B737-300 HAD AN AUTOPLT MODE CTL ALT ALERTING SYS DEFERRED PER MEL. INBOUND CREW DESCRIPTION OF DISPLAY WINDOW DEFECT INACCURATE.

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FLT CREW INBOUND INTO ZZZ HAD ACARS DEFECT OF 'ALT ALERT WINDOW ON MCP INOP ON BOTH AUTOPLTS AND ALSO WITH AUTOPLTS DISENGAGED. HAD CONTINUOUS ALT WARNING GOING OFF IN DSCNT.' ALSO NOTED THAT THE 'ALT HOLD DID CAPTURE DURING CRUISE FLT.' AFTER DEBRIEFING THE INBOUND CREW; IT WAS FELT THAT THE PROB WAS WITH THE ALT ALERTING SYS. THE DISCREPANCY WAS DEFERRED PER THE MEL. DISCUSSED WITH THE OUTBOUND CREW; AND THEY REQUESTED; WHEN ACFT ARRIVED IN ZZZ1 THAT OUR MAINT FOLKS SEE IF THEY CAN FIX PROB BEFORE THEY HEAD ON TO ZZZ2. I AGREED WITH THE CREW AND NOTIFIED ZZZ1 OF THE PROB COMING IN; AND SUGGESTED HAVING AN MCP PANEL ON HAND IN CASE IT WAS REQUIRED. AFTER DEPARTED FROM ZZZ TO ZZZ1 AND FLT CREW SENT ME AN ACARS MESSAGE; NOTING THAT ALL INDICATIONS WERE NORMAL; NO DISCREPANCIES AS PREVIOUSLY RPTED. I UPDATED THE CURRENT DEFERRAL WITH THE CREW'S COMMENTS. DISCUSSED PROB WITH AVIONICS TECHNICIAN IN ZZZ1 AND WE BOTH AGREED IF NO PROBS WERE FOUND DURING BITE TESTS; THAT THE DEFERRAL WOULD BE CLRED AND NO NEED TO REPLACE THE MCP PANEL. LATER ON THE TECHNICIAN CALLED BACK AND INFORMED ME THAT THERE WAS AN INTERMITTENT PROB WITH THE MCP ALT WINDOW CHANGING FROM 10000 FT TO FL500 WITHOUT ANY PWR INTERRUPTIONS. HE INFORMED ME THAT HE TRIED A NEW PANEL AND THE INTERMITTENT PROB WAS STILL PRESENT. AFTER MUCH DELIBERATION; NO RELIEF WAS FOUND IN OUR MEL; FOR THAT PROB THAT WAS NOW PRESENT. I HAD THE ACFT GNDED FOR THIS PROB AND A NEW WRITE-UP CREATED TO REFLECT THE PROB AND THE CURRENT DEFERRAL CLRED; IN ORDER TO AVOID CONFUSION ON WHAT THE REAL PROB MAY HAVE BEEN ORIGINALLY. REVIEWING WHAT OCCURRED; I SHOULD HAVE FURTHER QUESTIONED THE ORIGINAL CREW'S DISCREPANCY; IN PARTICULAR THE COMMENT OF 'ALT ALERT WINDOW' THIS STATEMENT LED ME TO BELIEVE THE PROB WAS ASSOCIATED WITH THE ALT ALERT SYS; BUT THEN AGAIN ON THE GND IN ZZZ NEITHER CREW RPTED THE ALT WINDOW JUMPING TO FL500 AND OUTBOUND CREW RPTED NO PROBS.