Plot hole: Caroline helps Max get her degree, since Max didn't graduate high school. However, in episode 5 of season 1, Caroline and Max are raising money to pay off Max's student loans.
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.