MD88. CREW NOTED AN 'ACCESS COMPARTMENT DOOR' MESSAGE WARNING LIGHT ON COCKPIT SETUP. AFTER TKOF A NOSE GEAR DOOR WOULD NOT CLOSE.

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MAINT HAD WORKED ON THE ACFT DURING THE NIGHT. PRIOR TO DEP FROM THE GATE (IE; PUSHBACK) I NOTICED THE ACCESS COMPARTMENT DOOR MESSAGE ON THE COCKPIT SETUP. THE MECH HAD ALREADY LEFT; I CALLED FLT CTL DISPATCHER AND THE MAINT COORDINATOR TO ATTEMPT TO CORRECT THE PROB. WE WERE UNABLE TO EXTINGUISH THE MESSAGE; BUT COMPLIED WITH THE MEL. I OPENED THE NOSEWHEEL DOORS AFTER CONSULTING WITH THE MAINT COORDINATOR AND ASKED HIM IF IT WOULD BE OK TO LEAVE THE NOSE GEAR DOORS OPEN. HE AGREED; BECAUSE THE DOORS SHOULD CYCLE WITH GEAR RETRACTION. ON TKOF AT GEAR RETRACTION WE EXPERIENCED A LOUD VIBRATION WITH THE GEAR UP. WE PUT THE GEAR DOWN AND THE VIBRATION STOPPED. WE COULD HAVE RETURNED TO DAB BUT I COORDINATED WITH FLT CTL TO DIVERT TO MCO SINCE MCO IS A MAINT STATION AND WAS ONLY 45 NM AWAY; FLYING TIME 20 MINS AND DAB IS NOT A MAINT STATION. UPON ARR AT MCO A NOSE GEAR DOOR WAS FOUND OPEN. IT DID NOT PROPERLY CYCLE WITH THE LNDG GEAR RETRACTION. AT NO TIME WAS THE SAFETY OF THE FLT IN JEOPARDY.