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.
Trivia: In the part of the movie that begins with Valentine's Day, there's a shot of a store with a heart (and other Valentine's decorations) in the window. Pasted on the heart is a black silhouette of a man and woman looking into each other's eyes. If you look closely, you'll notice the silhouette is of Tom Hanks and Meg Ryan.