A B737-400; ON ENG START; THE START SWITCH DID NOT RELEASE AND THE START VALVE REMAINED OPEN. MANUALLY MOVED START SWITCH PER QRH.

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DURING ENG START ON #1 ENG (I THINK); THE START SWITCH DID NOT RELEASE AND THE START VALVE OPEN LIGHT REMAINED ON. WE COMPLIED WITH THE PROCS IN THE QRH. WITH THE START VALVE OPEN LIGHT OUT AND THE ENG RUNNING NORMALLY; WE CONTINUED THE FLT AND WROTE THE PROB UP AT DEST. SUPPLEMENTAL INFO FROM ACN 625829: WHEN I INFORMED THE FLT CREW THEY SHOULD HAVE HAD THIS PROB ADDRESSED BEFORE LEAVING ZZZ2; THEIR RESPONSE WAS THAT EVERYTHING FUNCTIONED NORMAL; THE START VALVE OPEN LIGHT WENT OUT WHEN THE START SWITCH WAS ROTATED TO OFF; INDICATING THE START VALVE WAS CLOSED; AND THEY HAD NO OTHER PROBS. THE FLT CREW INADVERTENTLY ASSUMED THAT THEY COULD DEPART ZZZ2 WITH A KNOWN ACFT DISCREPANCY; WHICH REMOVES THE AIRWORTHINESS OF THE ACFT; BECAUSE NO MAINT WAS REQUIRED. THIS IS AGAINST COMPANY POLICY AND FAA REQUIREMENTS. MAINT CTL SHOULD HAVE BEEN NOTIFIED AND ENRTE MEL 80-2B ISSUED IF POSSIBLE. I DO NOT BELIEVE THE FLT CREW INTENTIONALLY VIOLATED COMPANY POLICY AND FARS; BUT LEAVING A STATION WITH A KNOWN ACFT SYS PROB IS NOT ALLOWED AND FLT CREWS SHOULD BE AWARE OF THIS.