OK, so I think the errors are the editor's way of complaining that there were resources, in general, which were not freed upon exiting the application.
For instance, doing something like...
var local_scene = null
var resource = load("res://MyScene.tscn")
local_scene = resource.instance()
# Ignore responsibility for freeing 'local_scene'
...seems to trigger the two errors. But it can be resolved by calling .free() on the variables using instanced resources:
Additionally, it seems like .queue_free() might NOT work in some cases. I will update my findings when I learn more.
Any comments, corrections, or feedback in the meantime would be appreciated.