When Guy is on the train returning to Metcalf (after the tennis match) you can see over his shoulder that the sun has almost completely set - but the next scene shows Bruno (in line to go back to the island) looking up to see the full sun in the sky.
When Miriam's glasses drop to the ground as Bruno strangles her, they land softly on the grass and don't break. However after the struggle, when he reaches down to pick them up they are seen to be cracked in one of the lenses.
When Bruno arrives at the Metcalf train station with the cigarette lighter in hand, a background sign for "Ray's Danbury Diner - Low Prices" can be glimpsed in the background. (The scene was filmed at the Danbury train station.) A minute later, the sign reads "Ray's Metcalf Diner".
During the Forest Hills tennis match, Guy's shadow moves from behind him, to in front of him, to his left, and to his right, even within a given game. Curiously, his shadow is always long, regardless of direction, so none of these shots were made during midday.
When Bruno gets back into his boat after strangling Miriam, he sits down and pulls a lever to put the boat in reverse. At this point you can clearly see a harness attached to the stern tighten and pull the boat backwards from the dock.
When Bruno takes a taxi from the Anthony house in Arlington, Virginia, to travel to Union Station in Washington, the taxi crosses a bridge over the Potomac River, which separates Virginia and Washington, D.C. The taxi is crossing the bridge in the wrong direction, because the Lincoln Memorial and Washington Monument (located in D.C.) are shown through the rear window of the taxi.
Early in the film, when the train pulls into the station, the NHRR coaches are the newer, smooth sided coaches, commonly referred to as American Flyer Coaches, because they were modeled by American Flyer, which was located in New Haven. When the passengers exited the train, the coaches were the older coaches, referred to as Heavy Weight Coaches.
When Bruno drops the lighter down the sewer, he tells the bystanders, he needs help retrieving his cigarette CASE. Perhaps Bruno thought it would sound more important if he said he'd dropped a case rather than a mere lighter.
When Hennessey and Hammond follow Guy to the station, they see him at the ticket booth. As they carry on to follow him, several people in the background walking through the station and going up the escalator can be seen looking and pointing towards the camera and crew.
When the detectives lose Guy outside the Forest Hills tennis stadium, they are shown standing on a curb, with a black car parked down the street behind them, before Hennesey dashes out across the street and flags down another vehicle. When he jumps in and asks the woman in the back seat to let them follow Guy's cab, the same street and parked black car are seen through that vehicle's rear window, even though that car was plainly stopped coming from a different street and a different direction.
When the two body guards are chasing after Guy, they stop on a street where the shadows in the background are cast to look like the sun is shining from above. However, when the two body guards are standing next to each other, they cast shadows on each other as if the light is coming from the front of them.
When Guy arrives in Washington D.C. at night, the illuminated capitol dome is visible in the background. The dome 'vibrates' (compare with tree in the middle ground), revealing the shot to be assembled footage.
The goof item below may give away important plot points.
As Bruno is hurrying back to his boat after strangling Miriam on the island, he passes other couples laying on the grass as the voices of Miriam's boyfriends are heard calling for her. When the boys find her dead and begin shouting for help, these bystanders jump up in alarm and react to their cries. But many of them jump up several seconds earlier, while the boyfriends are still heard playfully calling Miriam, clearly because the soundtrack and the film were not matched and edited properly.