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).
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.