Factual error: Opening scene shows NYC 1962 as a 1964 Chevy Impala rolls by.
Factual error: The chicken they eat in the car is Extra Crispy Kentucky Fried, not Original Recipe. Extra Crispy wasn't introduced until the late 70s.
Factual error: Male "chorus" watching 6th game of 1962 World Series all applaud Roger Maris' home run, shouting "this means no 7th game" as they invite Viggo Mortensen to join them in front of the TV. However, the HR only cut the Giants' lead to 3-1, as Billy Pierce pitched a masterful 3-hitter to beat the Bronx Bombers 6-2 and force a 7th game the next day. The gang might have been pleased, but hardly ecstatic, down by two runs in the 5th inning. Moreover, while the Yankees won Game 7 the very next day (1-0, in San Francisco) to capture the title, that same evening (October 16) was also the beginning of the Cuban Missile Crisis, though the American public was not made fully aware of it until a few days later. This has important consequences for the film as a whole. In particular, when Tony Vallelonga returned home in time for Thanksgiving, as he had promised his wife, his family and close friends would be chastened and subdued by the events of the preceding month. Hence his reunion with Dr. Shirley (Mahershala Ali) would be poignant, but hardly festive. There was no joy in the Bronx, or anywhere else.
Factual error: Similar to the opening scene, as they pull into Macon Georgia, just before the tailor shop scene, he parks between what looks like a 1957 Ford station wagon and a 1964 two tone red and white Ford Falcon. Falcons were more rounded in 1962.
Factual error: The squad car that pulls them over in Louisiana in 1962 is a 1964 Chevrolet.