Revealing mistake: In the final scene when Annie and Sam are exiting the observation deck coming towards the elevators, the New York skyline backdrop which should be visible behind them is missing, and the entire sound stage wall can be seen beyond the observation deck safety railings instead. 'Although the exterior and lobby of the Empire State Building, 350 Fifth Avenue at 34th Street, are the real thing, a slightly larger replica of the Observation Deck was built in a hangar at Sand Point Naval Base on Puget Sound just northeast of - where else? - Seattle.' https://www.movie-locations.com/movies/s/Sleepless-In-Seattle.php. (01:39:35)
Continuity mistake: The bearded man sitting next to Jonah, on the flight to New York, is also seen sitting two seats away from Sam when he flies to New York chasing Jonah. The same guy is on two different planes at the same time.
Visible crew/equipment: In one shot when Annie and Walter are speaking in front of a shop window, you can see the cameraman's reflection. You even see him pivot his torso to follow the actors as they walk offscreen.
Factual error: While Meg Ryan is typing her letter to "Sleepless and Son," Rosie O'Donnell is sitting on the couch watching "An Affair to Remember." Any true AAtR fan can easily notice that the film's editing has obviously been altered by the Sleepless director - the scene with Deborah Kerr and Cary Grant leaning on the boat railing actually takes place towards the beginning of the movie, while the scene of them looking up at the Statue of Liberty takes place about four days later. However, in Sleepless, the order of the AAtR scenes shown on Meg's TV are incorrect - Kerr and Grant are leaning on the railing as the sequence starts, then jumps WAY ahead to them staring up at the Statue of Liberty (which then would have been about four days later), and ends with them standing next to the boat's railing again (four days before).
Continuity mistake: When Jonah and Sam are seeing Victoria off at the airport, where does she go? During the scene other people are moving towards and around the door that Victoria seems pointed towards; however, in the shot that immediately follows her departure the doors are opened by the flight crew and passengers (including Annie) disembark. (01:04:15 - 01:05:25)
Factual error: Sam and Jonah go by motorboat from their houseboat that is moored on Lake Union to Alki Beach in West Seattle. Annie follows in her rental car, watching them from her vehicle "the entire way." This is impossible. To get from their houseboat by boat to Alki Beach (near where I live) involves going over the lake, through the Ballard locks, and across Elliot Bay (Puget Sound). The only road into West Seattle and to Alki Beach from the city does not follow their water route, and it is further south and goes over the West Seattle bridge - some miles from the lake and too far away for her to be able to see them on the water. The boat ride to the beach would also take over an hour with the wait to go through the locks, though they appear to reach it much sooner.
Plot hole: When it's learned that Jonah has taken a flight to New York by himself, the panicked adults never think to contact United Airlines, the New York Police Department, port authorities, airport security, the taxi companies, or the Empire State Building staff to alert them that an unaccompanied minor child is headed their way. Instead, Sam hops on the next flight to NYC to search for Jonah by himself. Considering the many hours Jonah waits on the Empire observation deck alone, it is apparent that none of the above knew he was there.
Continuity mistake: Annie is discussing her trip to Seattle with Becky at her house. She pulls out the tape of "An Affair to Remember", walks into her kitchen, and Becky puts Annie's things on the table, handbag on the left and the purse to the right. They go back to the living room, then return to the kitchen a couple of minutes later. In the shot when Annie puts her mug down, the purse is now on the left and the handbag is on the right. (01:12:40 - 01:14:30)
Factual error: Jonah points to the LP record and tells Sam that "Paul is dead" can be heard when the record is played backwards. He is not holding a Beatles' record, however, as can be seen from the album's label. In the US, the Beatles recorded under Capitol Records, and their labels had a multicolored circular band printed on both sides. This label is red.