CE-680A Captain reported it is possible to have the exterior paddle handle not stowed but still see the lock flags inside and be able to complete the door override procedure with no CAS alerts for the cabin door. With the exterior paddle handle partially open; the airflow could pop it fully open and the lock pins could be removed from the door jam; potentially causing the cabin door to open in flight.

Narrative

On this morning we arrived at the aircraft which was parked in the same place we parked it the night before at the FBO ZZZ. We noticed the main cabin door was already open and upon entering the cabin we were greeted by a detailing crew. Maintenance had been done on the aircraft overnight as observed by waypoint messages and a maintenance database manual left on the aircraft.We prepared the aircraft and PIC did the exterior preflight. I was SIC on this flight. Bags and passengers were loaded and when I went to close the main cabin door it appeared to [be] abnormal as I didn't get the normal click of the vent door and the amber light did not extinguish. Person A also advised that the Cabin Door" and "Check Door's" amber Crew Alerting System (CAS) messages were present.We ran the QRH procedure and did the cabin door override. The main cabin door closed; we observed 6 flags in the sight glass; the amber CAS messages extinguished; I heard the click of the vent door closing and we observed a white "Check Door's" CAS message which means the monitoring system is INOP. This is deferrable and we deferred it per a call to Maintenance and the MEL. We opened and closed the door 1 - 2 more times as we were waiting for a release as the system was down complying with the MEL each time.We got the release and taxied out for departure. Upon departure I observe the cabin was not pressurizing and differential pressure was not increasing. I noticed this prior to 1500 feet AGL and that the cabin was climbing at the same rate as the aircraft. We agreed that we were not pressurizing and coordinated with ATC for delay vectors and a hold to burn off fuel to return to ZZZ and land underweight as we had been fueled for a previous trip that had changed. Aircraft landed without incident.We transferred passengers and bags to the new assigned jet. I was the one who finally closed the door on Aircraft X as we put it away before disconnecting the batteries. When I tried to close the door from the outside I observed that the paddle handle would not stow in the closed position. I then observed that the key lock was in the "lock" position which I had never seen before nor knew this could happen. The key in the lock position prevents the paddle from stowing. I am certain that this was the issue from the beginning and that either Maintenance or the cleaners had left their key in the door and when they went to retrieve it from an already open cabin door they turned the key to the lock position before removing their key.What is alarming to me is that it is possible to have the exterior paddle handle not stowed but still see 6 lock flags inside and be able to complete the door override procedure with no amber "Cabin Door" CAS message even though the handle is not stowed/flush. If we were in fact flying around with the exterior paddle handle partially open it could have ended up a serious issue if the airflow had popped it fully open removing the lock pins from the door jam and having a cabin door open in flight.Suggestions: Have Textron make the sensor in the paddle handle illuminate the "Cabin Door" amber CAS message if the paddle is not stowed and prevent the override procedure."