It certainly couldn't have taken NBC by surprise, since the word "Possum" was in the titles of both episodes. On Tuesday, the second episode of "Parenthood" ("Man vs. Possum") featured a storyline with series lead Peter Krause doing battle with a possum on his property. Two nights later, "Parks and Recreation" ("The Possum") brought us Fairway Frank, a four-legged critter who plagued a golf course in pseudo-"Caddyshack" fashion.
I'd say "Parks" got more mileage out of its possum — in terms of story and certainly in terms of comedy — though when yet another possum emerged later in the episode, I thought it was a bit inexplicable that the characters didn't try to capture him as well. However, though my attempt to make "just get the other possum" a catchphrase describing holes in a show's plot has yet to catch on, I'll still always remember Possum Week on the Peacock.
Update: Here's a possum-related deleted scene from last week's "Parks."