Plot hole: The episode partly revolves around Max having lied about the rent amount since Caroline moved in, but earlier in the series it was established that Max was never on the lease and thus didn't have to pay rent she couldn't afford (at least before the cupcake business took off). This was made explicit to Caroline multiple times, who presumably didn't pay rent either. They had the lease renewed with the original tenant in Season four, but that's not four years regardless.
Factual error: Caroline says to Max, "You've had rabies once," implying that she was infected with rabies and recovered. Rabies, once you get infected, is lethal and untreatable. (00:00:10 - 00:10:15)
Suggested correction: Rabies is curable if you are infected, as long as you don't show symptoms. You can get treatment - the sooner, the better. Also, the further away the wound that infected you is from your brain, the longer time you have until symptoms show.
Character mistake: Winona says that Jason killed a penguin on their trip to the Arctic. This is impossible because penguins only live in the southern hemisphere.