LJ25 CREW REPORTED THE ENTRANCE DOOR CAME OPEN AFTER TKOF.

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JUN/XA/01 AT XA00. I WAS ASSIGNED A NEW COPLT AND BRIEFED HIM ON HIS DUTIES AND WHAT I WANTED. I CLOSED THE CABIN DOOR AND MADE THE STATEMENT '2 HANDLES FORWARD.' I TOLD THE FO HIS RESPONSE WAS TO BE 'DOOR LIGHT OUT.' THE DOOR LIGHT WAS ON. I VISUALLY CHKED THE DOOR PINS WERE IN PLACE -- MUST BE A BAD SWITCH -- AND PROCEEDED TO TAXI. WHILE TAXIING; THE DOOR LIGHT WENT OUT 'MUST BE A BAD SWITCH.' XA20 AT HMR THE FO CLOSED THE DOOR AND RPTED '2 HANDLES FORWARD.' I REPLIED 'DOOR LIGHT ON; ARE YOU SURE 2 FORWARD?' HIS RESPONSE; 'YES; 2 FORWARD.' AS WE TAXIED FOR ABOUT 1 MI; THE DOOR LIGHT WENT OUT. 'MUST BE A BAD SWITCH.' XA15; RDD; THE COPLT WAS BUSY WITH THE 2 PAX AS I WAS GETTING READY TO START #2. HE CLOSED THE DOOR AND RPTED '2 HANDLES FORWARD.' MY RESPONSE; 'DAMN DOOR LIGHT STILL ON.' TAXIED TO RWY 16 AND WAITED FOR DOOR LIGHT TO GO OUT. 'I GUESS THE SWITCH FINALLY TOOK A DUMP; ARE YOU SURE BOTH HANDLES FORWARD?' HIS REPLY; 'BOTH FORWARD.' TKOF WAS NORMAL UNTIL JUST AFTER ROTATION AND GEAR WAS COMING UP; THE OUTFLOW VALVE CLOSED AND THE CABIN STARTED TO PRESSURIZE. THE TOP DOOR OPENED AND REMAINED OPEN. TURNED DOWN WIND; SLOWED ACFT AS MUCH AS POSSIBLE; LANDED; INSPECTED DOOR; CLOSED DOOR; MADE SURE HANDLES FORWARD; DOOR PINS CHKED AND THEN RETURNED TO VNY. CAUSE: FO WAS DISTR BY PAX AND DID NOT PROPERLY CLOSE DOOR; EVEN THOUGH HE DID USE THE ELECTRIC CLOSING MOTOR; DID NOT PUT TOP HANDLE FORWARD. CAPT WAS LULLED INTO BELIEVING DOOR WAS LOCKED BY THE 2 PRECEDING 'DOOR LIGHT ON AND GOING OFF DURING TAXI.' CORRECTIVE ACTIONS; CAPT ENSURES THAT DOOR IS PROPERLY CLOSED; EVEN IF IT DELAYS FLT FOR 60 SECONDS. FLT DUTIES COME FIRST; PAX COMFORT LATER.