Aesop Amnesia: Joked about by Mike — during the party scene, the kids blunder into three separate and consecutive pranks (all with exactly the same obvious kind of set-up), even right after laughing at the previous one.
Mike: ...So no one has any accumulated memory or experience?
Various riffs about Tony being a werewolf/dog, before the transformation.
Not a running gag in the episode itself, but Servo makes the quip: 'You get a lot of dirt with werewolf, you get a lot of clean with Tide.' It would later be used in Season 9 in the next werewolf movie... namely, uh, Werewolf.