When James and Joel are driving in New York, James smiles and looks out the car window. If you look above the car, you can see an advertisement for 'Sonny with a Chance' - a Disney show which wasn't even made until 2009.
In the New York City scene near the end, the pedestrian signals clearly showed the hand and walking man symbol, which were not used in New York City until the early 2000s. In 1987, the pedestrian signals in the city used text "Walk" and "Don't Walk" indications, rather than the symbols.
After James has a drink at the bar, he is driving past a car dealership, where you can clearly see new Ford Mustang models. And also at the end in New York City when he steps off the bus, a modern model Lincoln Town Car is clearly visible.
When Connell and James drive over to Connell's mother's house, Connell's car has a visible "You've Got a Friend in Pennsylvania" license plate. However, the car that Connell parks behind has a newer Pennsylvania license plate that was issued after 2000, despite the movie being set in 1987.
In the bus montage arriving in New York City, the modern (8th Ave.) New York Times building is seen from a vantage point of 12th Ave. The film takes place in 1987; the New York Times Building was built 2003-2007.
In the scene near the end where James, Joel and Frigo are sitting on the hill drinking, a stack of empty cans with the old-style pull tabs is seen next to James. Pull tab cans had been discontinued in the U.S. by 1987.
Joel asserts that the famous aphorism "Fortune favors the bold' was written by the Roman poet Virgil (Publius Vergilius Maro, 70-19 BC), but in fact, it was written by the Roman playwright Terence (Publius Terentius Afer, 185-159 BC) in his play Phormio. The phrase is often associated with Virgil's epic poem, the Aeneid, appearing in book 10 line 284, in a slightly different form. The overeducated Joel should know better.
When James is calling the horse race for the second time, when the camera shows the horses the purple horse is in the race but when the camera closes up on James, the purple horse is still in the home/stationary position, but when the camera shows the horses returning to the home position the purple is moving back again.
Emily's Pacer: In scenes while driving the car has dark diamond style cloth/vinyl seats, but in scenes where you see the whole car / it is parked, the seats are all light brown with no diamond like pattern.
When James applies for a job at Adventureland, he is wearing both straps of his backpack during the first shot, but in the next shot he's wearing only one strap on his right shoulder. This error repeats when he first speaks to Bobby.
When Em Lewin sits up from laying down in her bead (in the scene when 'I Want Action' is playing), she lifts her head straight up. The camera angle switches and suddenly Em's head is tilted and resting on her shoulder.
Near the end of the movie after James finds out about Em & Connell, Wang Chung's "Dance Hall Days" can be heard playing over the park's loudspeakers. If you have subtitles on, the subtitle states "Safety Dance" (by Men Without Hats) as the song playing.
When James and Em are talking during the party at Em's house, "I'm in Love with a Girl" is playing on the turntable, which is the last song on Big Star's "Radio City" album. However, the record is actually playing the second groove, which is the song "Back of a Car."