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.
Continuity mistake: In the scene where Guy enters Bruno's house to kill his father, Guy takes out a flashlight to look at Bruno's map. In one shot, you can only see the map, and the light is very small and circular, but in a wider shot of Guy's upper torso, the light covers most all of the map.
Other mistake: When Bruno returns to Metcalf to plant the lighter at the fairground, the passenger to his right in the club car asks for a light. Bruno carefully offers him a matchbook, rather than the crucial lighter. Guy Haines travels back to Metcalf by a different train, but the same man is sitting to his right in the club car - just slightly further away. Either this guy can travel on two trains at once, or there was a bit too much economy with the bit part actors.
Factual error: Several seconds into the opening of the second scene, the train pulls out of Union Station headed for NYC. A date palm or other palm tree is visible growing on the left side of the train tracks. Palm trees don't grow in Washington DC, but they do in LA where I suspect this footage was filmed.