Yeah, TN gets a few gators from "pet" dumpers, and maybe migration. Never heard of any over here in E. TN, although maybe the occaisional escaped python or boa.
Now...almost every winter we do get pacu & pirahna showing up at the output of the Bull Run Steam Plant (where the water is warm). Morons arround dump them when they get too big or agressive in aquariums.
From what I understand, in recent years the most problematic exotic I think we have (besides carp & milfoil) is zebra mussels.