When Jaime drinks a cappuccino, she gets foam on her nose. The shape of the foam changes significantly between shots.
Jamie says she wanted to be an Irish literature major at Harvard. Irish literature is merely a single course at Harvard, not a major.
Tom is on the other side of a glass door when Jaime is fabricating an explanation to Professor Samuels for breaking into his office, so he couldn't possibly have heard the details she gave him, and wouldn't have been able to back up her story.