A B737-300 DURING CLB TO 10000 FT THE ACFT WOULD NOT PRESSURIZE. REMAINED AT 10000 FT TO TRIP TERMINATION. FOUND FORWARD ENTRY DOOR NOT SEATED.

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ON DEP; WE NOTICED THE CABIN ALT WAS CLBING FASTER THAN NORMAL. WE QUICKLY CHKED THE BLEEDS AND PACKS AND THEY WERE ON AND AUTO RESPECTIVELY. ALL DOOR LIGHTS AND PRESSURIZATION LIGHTS WERE NOT ILLUMINATED. AS WE CONTINUED TO CLB; THE CABIN DIFFERENTIAL PRESSURE STOPPED AT 1.0 AND THE CABIN ALT CONTINUED TO CLB. WE ASKED FOR AND RECEIVED A TEMPORARY (AND LATER FINAL) LEVELOFF AT 10000 FT. THE CABIN STABILIZED AT 1.0 PRESSURE DIFFERENTIAL AND 7500 FT CABIN ALT. PACKS TO HIGH MADE VERY LITTLE DIFFERENCE. WE TALKED TO THE FLT ATTENDANTS AND THEY CONFIRMED AN AIR LEAK AROUND THE FORWARD ENTRY DOOR. I ASKED THEM TO TAKE THEIR SEATS FOR THE REST OF THE FLT AND WE CONTINUED TO ZZZ BECAUSE WE HAD NO WARNING LIGHTS AND; BY THIS TIME; WE WERE AS CLOSE TO ZZZ AS WE WERE OUR DEPARTING CITY. MAINT MET US AND NOTICED THE FORWARD ENTRY DOOR WAS NOT COMPLETELY SEATED AS WE TAXIED IN. THEY ADJUSTED THE DOOR AND PERFORMED A PRESSURIZATION CHK (NORMAL). AGAIN; NO WARNING LIGHTS OR HORNS FOR THE ENTIRE FLT.