Your looking at the duct where it has no flange between the homemade hood and the duct..nice 3 inch gap there...notice the wooden floor of the upstairs tenant there.....there are zero filters installed in this 10 ft hood.....now take a look at the power cord of the fan running straight up the inside of the duct...notice the scorched, grease laden ceiling above the grill area.....
In picture two does it look like a rodent carcass...are those cockroach legs there too?
I don't see the problem, that electric cord is suppose to be running through the duct and hanging out the bottom of it like that....what's the big deal?