Other mistake: Mike and Axl suggest to Brick that he find "some poor schmuck" that his girlfriend can torment, so she will stop bothering Brick. After the plan works, Frankie states in a voice over that "Damn, I'm good", implying that it was she who suggested this tactic to Brick. (00:27:15 - 00:30:00)
Other mistake: When Brick first goes to see Betty White in the library, she gives him until Walt Whitman's birthday (May 31st) to return the books. When he returns and realises he is still short 1 book, she gives him until Sir Arthur Conan Doyle's birthday which is May 22nd - before Whitman's birthday.