At the end of the movie supposedly Sam and Jonah have returned to the top of the Empire State Building to retrieve Jonah's backpack. Yet when they enter the elevator to go back down no one (not Sam, not Jonah, not Annie) has the backpack.
When Jonah is sitting with Jessica in the chair, he tells Sam: "When you play it backwards this says 'Paul is Dead'." The actual saying is 'Turn me on dead man' and it is on The Beatles' White Album, which was released on Apple records. (The record on their record play has a 'Capitol' label on it). The Capitol record that they are playing is more likely Strawberry Fields Forever. In the end section people claimed they heard John sing,"I buried Paul" which contributed to the hoax of Paul's premature death.
When Annie first starts walking along the observation deck of the Empire State Building after it's closed for the evening, she passes a telescope that has its eyepieces facing the camera. A moment later, as she's walking towards Sam and Jonah, she passes the same telescope, but now it's facing a different direction. That would be hard to do considering that the deck was closed and Annie was the only one out there prior to Sam and Jonah arriving.
On Valentine's Day in New York, while Annie and Walter are having dinner, the sky is getting dark. Then, it is lighter when Sam is leaving the airport. It is darker again when Jonah is shown on top of the Empire State Building.
During the scene at the Rockefeller Plaza when she drinks champagne with Walter, the champagne glasses are not consistent. When the camera is on him, the champagne has bubbles and glasses have condensation. When shots are on her, champagne is flat and there is no condensation.
When Sam and Jonah take the small motorboat to Alki beach, they could not have gotten from Lake Union where the houseboat is moored to Alki in West Seattle without going through the Ballard locks. Possible but highly unlikely in a small outboard like they were using.
The unaccompanied minor age with most airlines is 17 and under. At Jonah's age (8), with an unaccompanied minor status, he would have needed a parent/legal guardian/authorized adult at the departure gate and at the arrival gate. Jonah would have also have had to wear a placard around his neck with all his info and parent signature during the entire flight.
Though it would have ruined the climactic end to the movie, it would have not been necessary for Sam (Tom Hanks to frantically hop the next plane to New York in an effort to find his son. Jonah's plane had just taken off from Seattle when Sam learned where his son had gone. Sam had hours to notify authorities concerning the safety of his son, a young child. A simple call to the airline and the pilot would have been notified that the Jonah was on board and the situation. Airport officials could have put him on a plane right back to Seattle upon arriving in New York or held him at the airport until Sam arrived to claim his match making son. Even if Jonah had already landed in New York and was patiently waiting at the Empire State Building, a phone call to the Manhattan Police or the security at the Empire State Building would also have gotten adult supervision for young Jonah instead of the little boy sitting alone at the top of the Empire State Building in the winter cold all day long.