The recirculation flap can fail in the open position if the small vacuum motor fails, if the vacuum line to that device slips off a connector or if the spring holding the door into the cabin shut either breaks or cuts through its plastic mounting point. If the spring is in place and the door is ajar, then the vacuum device in the evaporator box has stopped working for some reason. I've seen them with a hole worn in the plastic, with the device mounting broken and with the vacuum line slipped off.
While your sheetmetal screw will keep the door closed, thereby stopping the fogging of windows on cold days, the opening is important for air conditioning efficiency during warm weather, so you should figure out what is wrong and fix it.
If you have bad odors from the HVAC system it can be from a plugged drain in the evaporator box. The drain for the box is quite small. It drains out on the passenger side of the transmission just behind the larger drain that evacuates the entire HVAC cavity below the winshield. I've heard of folks unplugging the evaporator box drain tube by using compressed air and by running something like string trimmer string into it.
