In the first classroom scene there appears to be a dark haired woman with a man in a sweater sitting behind her, sitting next to Spence. It seems as though Spence is looking at her. Moments later both her and the man are gone from the chairs.
When Doug comes down the stairs to read his book with Carrie he has the book with him. The book disappears as he goes through the items he brought down with him. They realize he forgot the book so he runs back upstairs to get it.
In the introductory class the course leader includes Jane Austen in his list of Victorian writers. When Victoria was crowned in 1837 not only had Austen been dead for 20 years but the throne had passed hands three times in that period.
When Carrie is confronting Doug in the bedroom about his faking in class (telling him how obvious it was) a crew member can be seen moving reflected in the window behind her.