When Irving leaves Polito's house, his comb-over switches sides.
The opening scene indicates the date is April 28, 1978, but shortly after on the video surveillance, the cameras show the date as April 26, 1978.
In the opening scene, the FBI surveillance agents are using a ReVox 2-track tape recorder. In a later flashback to that scene the tape recorder is a Teac 4-track recorder.
During the first confrontation between Rosenfield and DiMaso before they meet the mayor, the briefcase of money behind them is open. When DiMaso goes over to it, he clicks open the catches.
(at around 1h 12 mins) Irving's automobile is introduced as a blue 1977 Cadillac Eldorado. However, when Irving and his wife meet Mayor Polito and the casino financiers, Irving pulls up in a 1978 Cadillac Eldorado of the same color. You can tell it is a 1978 model because it has a thicker, boxier grille.
According to Christian Bale, much of the movie was improvised. So, during the shooting of the film, he noted to Writer and Director David O. Russell, "You realize that this is going to change the plot greatly down track." To which Russell replied, "Christian, I hate plots. I am all about characters, that's it." This 'technique' of Russell's caused the characters to hesitate at times when speaking and often created extended pauses or silence in the dialogue which gave the plot of the film a very amateurish 'feel' because of the improvisation.
Sydney wants Irving to flee with her to Estonia or Romania. At the time Estonia was solidly part of the Soviet Union and Romania was a brutal Stalinist dictatorship. Neither would have been necessarily impossible to get to but seem dangerously impractical destinations for Sydney to even consider, even with the law on her heels.
Bradley Cooper calls his boss and asks "Where are you?" several times. In 1978, before cellphones, if someone answered the phone, you knew exactly where they were.
When Irving gets into the safe to get his gun, the stacks of $100 bills are of the new type that was not put into circulation until the late-1990s.
Stoddard Thorsen wears a Rolex 116718 GMT Master II wristwatch, which was first manufactured around 2010.
At the end of the movie, when Rosalyn is talking about the car accident in her neck brace, you can see the cameraman and camera in the reflection of her sunglasses.
The airport shown as Teterboro in New Jersey is actually the Norwood Airport located in Norwood Mass.
Sheik Abdullah/Paco Hernandez (Michael Pena) offers to shake the hand of Victor Tellegio. The 'sheik', being a Muslim, would never shake the hand of an 'infidel'. Either it was a goof or a revealing error, possibly indicating that Hernandez did not know Muslims don't shake hands with non Muslims.