When Simon comes downstairs wearing Courtney's robe, he gets a beer out of the fridge and takes the bottle cap off. When Courtney asks him for her robe, and he starts to take it off, the bottle cap is back on.
When the group is driving back to Harvard after seeing Simon's son, Simon yells out to stop the car. Just before the scene changes, you can see out the driver's window, and hear, that they are on a fairly busy highway. When they pull over to stop, they are on a sparsely populated road with no traffic.
In the courtroom, Simon says he was not trespassing because Harvard is a Land-Grant School. Harvard is a private institution. The state's land-grant college is the University of Massachusetts at Amherst.
After Simon is evicted from the library basement, Monty says he needs a home. Simon replies that he had a home, "with 17 bathrooms and 8 miles of books". Since he is penniless, presumably he is referring to the library he left. But Harvard's Widener Library has nearly 60 miles of books, not 8.