Plot hole: Farley Granger meets a math professor on a train bound from New York to Washington, and is able to prove as much to the police. The professor got on in New York and got off in Wilmington, DE, while Granger boarded the train in the fictitious town of Metcalf, NJ, and rode on to Washington. Thus, they met between Metcalf and Wilmington. But the police say Granger could have boarded the train in Baltimore, by which time the professor would have gotten off and they never would have met.
Plot hole: If Guy was in such a hurry to get out of there, couldn't he have much more easily lost the match in three sets? Surely, a match loss would be a small price to pay to alleviate a murder charge.
Plot hole: Anyone of Anne's wealth and position would have insisted that Guy get advice from a lawyer. Even if Guy somehow refused to go himself, she would have gone to one. There's nothing to lose by going to a lawyer and everything to gain, and there's no way she's never thought of it, given her father's job.
