Moments before Susan suggests to Joe that they go to Boston because it's Saint Patrick's day there (17 March) and no one will be looking for him, they are driving past autumn foliage.
When Susan and Joe leave the airport by bus, the police cars that have just arrived are parked about 20ft from the bus. The bus pulls away as the two of them begin to talk. After a bit of talk we see that the bus had only traveled about 10ft despite previous shots establishing otherwise.
After he supposedly kills his friend in his apartment, he has blood on his hands. The blood dries. When he is on the subway, he scratches his nose and his hand is clean. In the next shot, his hand has blood on it again.
The date is established as early March in New York City yet the trees are in full bloom.
Campbell Scott's glasses disappear between shots when he is in line at Logan Airport in Boston.
Joe's calendar says "Friday, March 12, 1997." March 12, 1997 was a Wednesday.
At about the halfway point, when Susan is showing Joe her snapshots of the trip, she refers to one image as 'the mystery man with his lovely companion.' When Joe realizes that is is the same woman in the perfumery (by seeing the two photos side by side), the woman's face goes from an indecipherable blob of pink, about the size of a pinky nail, to a clear image. There is no evidence of Joe using anything but his naked eye to discover this, yet a human eye is incapable of clearly magnifying an image so much (over 15x).
The Spanish Prisoner (the confidence scheme) is a very well-defined scam in which the victim is tricked into sending money somewhere in the hope of receiving a lot more money in return. "The Spanish Prisoner" (the movie) portrays a scheme that bears no resemblance (absolutely none) to the scam for which the movie was named. The scam in the movie is a more of a complicated blackmail scheme.
The view on the hotel's security monitor pans a bit to follow the movement of someone on the boat dock, which a fixed security camera cannot do.
When Susan and Joe are walking away from a hotel, there's a noise of a plane flying overhead and away from them (The Doppler effect is used). However, the next scene shows a seaplane flying parallel to them at a distance. That plane could not have made that noise.
When Joe signs the form at the club the top of the document is obscured. The text of the document is visible and refers to joining the Knickerbocker club. Then the police show it what is supposed to be the same document the text is different, and in Spanish.
When Joe Ross makes his way through the carousel, a movie light can be seen in the background with a crew member and cases also visible for a few moments to the right of the light.
Immediately after the business meeting at the start of the movie, as Joe and Mr Klein are walking along the beach, the furry cover on a boom mic can be seen dipping into view several times from overhead (TV version).
When the rendezvous in Central Park is set up, Scott is told to go to the Navy Fountain. The fountain that he goes to is actually the Bethesda Fountain.
Jimmy and the feds could not have known Joe would get on that ferry.
McCune could not have known Joe was going to Boston.
When Joe goes to Rebecca's apartment and she calls in sick, she leaves a voice-mail saying "This is Susan Ricci[...]" rather than her character's name.