Right before the fight scene in the bowling alley, Gatsby Boy bowls a strike. However, when Hopper charges down the alley after him, the 7 pin is shown still standing.
The movie starts in December, 1942, and when Sean Penn goes to the movies, there is a newsreel discussing the "Teenage Draft Bill." The first peacetime draft was authorized by Congress in September 1940, and a bill passed November 11, 1942, lowering the draft age to 18, which would be that "Teenage Draft Bill". Yet, the copyright of the newsreel is clearly 1937, 4 years before that bill. Obviously, the newsreel is a mixture of a different title screen from that of the newsreel.
The bodies of war dead were not returned home in WWII as depicted. War dead killed overseas in WWII are interred overseas.
While sitting at a table talking with Henry, we see Nicky (Nicolas Cage) light a cigarette by striking a match on the back of a matchbook, however in 1942 matchbooks were front-strike until a new regulation in 1973 deemed front-strike too dangerous.
The railroad cars behind the steam locomotive are too new for the era the movie is supposed to portray (1940s).
The morning that Elizabeth McGovern asks Sean Penn out for Christmas Eve, Sean Penn is watching a F4U Corsair, which he misidentifies as a P-47. Yet, the Navy does not get any Corsairs until December 28, 1942. So Sean Penn could not have seen a Corsair before Christmas, 1942.