The book that inspired Rosalyn, "Power of Intention" by Wayne Dyer was written in 2004.
When Irving leaves Polito's house, his comb-over switches sides.
Stoddard Thorsen wears a Rolex 116718 GMT Master II wristwatch, which was first manufactured around 2010.
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.
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.
When Sydney is telling Richie that she isn't British, the positions of her curlers change multiple times throughout the scene.
When Irving and Carmine are outside The Plaza Hotel you can clearly see the Bergdorf Goodman Men's Store across the street on the east side of Fifth Avenue. The Bergdorf Mens store did not move there until 1990.
The blue necklace lights on NYC bridges were installed during the Manhattan Bridge Reconstruction Program in 1982.
The movie mentioned "The Boys and Girls Club" but it didn't become that until 1990. In the 1970s it was just the Boys Club of America.
When Irving collapses after leaving Carmine's house, after telling the latter that the FBI are involved in the scheme they are working on, Sydney runs towards him, coming out of the blue car. As she comes out of the car she leaves the door of the car open at such an angle that it could not possibly close by itself, nor does she close it, nor does she push it in any way to make it close. Yet, we hear the door closing, and when she takes Irving back to the car it is indeed closed.
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.
Arriving at Teterboro Airport, in the background are Diamond Aircraft. They were not produced until 1992.
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.
At the tape-recorded interview in Amado's office, a suitably vintage cassette recorder is used, however the cassette tape is of a design used by TDK in the late-'90s/early-2000s, and the microphone used most closely resembles a model produced by Radio Shack in the '80s.
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.
A Commodore 1701 computer monitor (introduced in 1982) can be seen during the 'videotaping members of Congress' scene in 1978.
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.
When Sydney and Irving discuss bank interest rates in his office shortly after first meeting in the early 1970s, Sydney curses Jimmy Carter for 12 to 18 percent rates, but Carter isn't President yet at this point in the story.
As the meeting between Victor Tellegio and the Sheik concludes, Tellegio tells Carmen that if they're serious, they'll transfer ten million dollars into an account and gestures with his hands. The camera angle changes and Tellegio repeats the same lines of dialogue with the same hand gestures but Tellegio's speech continues beyond what he said in the first shot, indicating it had been shot from two different cameras but not edited correctly.
In the opening scene, Irving Rosenfeld sets his comb-over with L'Oreal Elnett hairspray. While Elnett did exist in 1978, it was banned in the USA at that time. Elnett became available in the USA in 2008, when a packaging change allowed for Target to have a highly publicized exclusive Elnett US launch.
Sydney puts a colorful jacket on Irving in the dry cleaners. You can see clearly that when he hugs her from behind he still has the solid color blazer on.
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.
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.
(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.
When Sydney walks through the police station after being arrested in 1977, she passes FBI wanted posters for Patricia Hearst, who was apprehended in September of 1975, and Nancy Ling Perry, who killed by police in a shootout in February of 1974.
When Irving reflects on his childhood with his father's glass business (1950s), the windows being shattered are made of safety/tempered glass (which crumbles into granular chunks). This type of glass was not in standard use until 1966 and when we flash forward to the '70s, Irving picks up a piece of broken glass that is not safety glass.
After the 'science oven' fire the pattern of smoke damage on the kitchen cabinet door above the oven changes at various times during the film.
The sheik's private jet seen in the film, a Gulfstream GIV or V (they look virtually identical), didn't exist in the late 70s when the story takes place.
Throughout the movie are scenes with schoolkids wearing backpacks on the way to school, but school backpacks for kids were never in use during the 1970s.
The airport shown as Teterboro in New Jersey is actually the Norwood Airport located in Norwood Mass.
Long Black Road by ELO and Stream of Stars by Jeff Lynne were definitely not 70s tracks, both songs dating 2001 & 2013 respectively.
When Irving and Sydney are discussing Duke Ellington, she states that he died this year, that would have to make it at least May 24th of 1974 the day he died, yet the party in Long Island was in January.