that piece in the image goes into a hole in the heatercase where a control door is located. Since that piece came out on the passenger side you will need to use a flashlight and inspect the heatercase for a circular shaft that is flush with the heatercase and has a slot in it that that piece from the image needs to snap into. As for the noise concern that is the temperature blend door actuator
below is the image of the driver's side temperature blend door actuator. unfortunately i wasn't able to locate an exploded view of the heatercase to point out the location of the loose pin you had found ,so the best thing i can advise you on that would be to inspect the heatercase in the vicinity that you found the pin ,for the hole that it slides into.
on this model explorer you might be able to remove the driver's side inner forward flap of the floor console, remove the dash brace that bolts to the floor on one side and the dash on the top, you might need to remove the vent duct behind the brace, and with a 1/4'' micro ratchet with a shallow 8mm socket and with a 8mm gearwrench you might be able to get in there with small enough hands to replve the actuator without having to pull the dash.
I have just checked another '04 explorer and unfortunately for the loose pin you have, the dash might need to be removed to access the slot, at the very least the floor console will need to come out. I have located a vacuum actuator mounted to the side of the heatercase on the passenger side, just behind the climate control head , that actuates a lever like you had found. Viewed from laying underneath the passenger side dash and looking up towards the rear of the vehicle inside the dash, on the side of the heatercase, the vacuum actuators rod goes to the clip you are referring to, i am willing to bet that this is where the pin came from. My apolagies for the lack of detail in the pictures as there was not much room in the dash to get the camera angled right. I have circled the location where the pin would be(it would sit about behind the sideflap of where the dash wraps around in front and meets the floor console