Mr. Huck jokingly tells Hector, the other student taking the exam with Max, he'll see him in front of the ampm begging strangers for beer. There are no ampm convenience stores in Rhode Island.
In season one, Max payed her student loan and Caroline mentioned, looking through her papers, that she was studying arts, so she had to have graduated from High School.
During Max's graduation ceremony, Caroline steps outside into the hall to call Max's mother. While leaving a voice mail, Caroline's earning falls from her left ear and lands on her arm. After the phone call, the earring falls to the ground. On the bus ride home the earring is back in her left ear.