When Carl the janitor walks into the library, a poster advertising a college and career fair presented by Oakton Community College is visible on the door next to him.
The poster says the fair's date is Tuesday, February 19, 1980.
"The Breakfast Club" premiered on February 15, 1985, and was filmed in 1984, so by the time the students were in detention, the fair had long since passed.
February 19, 1980, was a Tuesday and Oakton Community College is a real school in Des Plaines, Illinois — where part of the movie was filmed — so in all likelihood, this is probably a real poster for an old event.