Audio problem: During the award ceremony when the (supposedly live) crooner sings Spanish eyes his lip syncing and the audio editing is awful.
Factual error: Despite the great effort (and expense) to recreate the 1950s through 1970s with vintage cars, SOHIO gas stations and a HoJos motel, none of the houses in any of the street shots show TV antennas on the roofs or chimneys. It's highly unlikely that every home on a given street used "rabbit ears." Cable didn't make inroads until the late 70s at best.
Continuity mistake: When Russ and Frank are in the hotel pool the woman in the left is holding a cigarette. In the close-up it swaps to a lemonade. Then in the wide angle it swaps back to a cigarette.
Factual error: When Frank takes Peggy to grocery store to beat that guy up, it takes place in Philly's Italian Market in south Philly. Meanwhile the street sign outside the store says Allegheny Ave, which is actually opposite side of town in north Philly.
Continuity mistake: When Frank walks in the restaurant to meet Angelo Bruno, he takes a sip, puts the glass down and says "sit down, Frank." From the opposite angle he is lowering his glass again.
Continuity mistake: When Frank tries to calm down Crazy Joe at the club after the Don Rickles show, Joe turns away twice.
Continuity mistake: When DeNiro kills Hoffa in the house, he is wearing white socks. In the later scene when they are going to place the box containing Hoffa in the incinerator, he is wearing black socks.
Factual error: When Mr. DeNiro made a call to "Mr. Hoffa" from a phone booth at a gas station in Ohio just before his flight to Detroit, you can see a rectangular, coin-operated box-type air pump. If this was the 1970's, I don't think gas stations were charging money for air...yet.
Factual error: When Frank plots the road trip he says they'll start off going up 476 to Pittston. In 1975, that road was called the Northeast Extension of the Pennsylvania turnpike. No one called it 476 until much later.
Continuity mistake: When Jimmy is sitting with Frank at the restaurant complaining about the fact that Tony Pro is late, we see Frank holding a Coca-Cola bottle with the right hand, but in the next shot the hand disappears from the table and stays down resting on the chair.
Continuity mistake: When the Sheeran's and the Bufalinos get in the car in Pittston, Carrie gets in on the left. In the next scene as they're starting the trip, Carrie is sitting on the right.
Other mistake: In the movie it is said that they're going to fly from Port Charlotte to Detroit, then drive to a meeting and back in three hours. Port Charlotte is in Florida. That timeline would be impossible. They meant Port Clinton Michigan.
Suggested correction: They never said Port Charlotte.
Audio problem: Just as Russell's wife opens her purse to get out a cigarette during the car journey, you hear the sound of a Zippo lighter being opened. Another lighter opens in sync with her actually lighting her cigarette.
Factual error: When they pull up to the house in the red Marquis to kill Hoffa, the front license plate has Michigan plates from 1973. Hoffa disappeared in 1975.
Continuity mistake: During the car trip to the wedding they were driving a 1978 Lincoln Town Car until they stopped at Howard Johnson's; after HoJos they were driving a 1975/76 Lincoln Continental: amongst other differences the front grills are different in those years.
Continuity mistake: When Jimmy is in prison, eating a dish of ice cream while having a conversation with Tony Pro, the amount of ice cream in the dish keeps changing: there's more ice cream, there's less ice cream, there's more. Every shot the amount increases, then decreases next shot. Also, sometimes you can see a cherry stem in the dish and sometimes there's no cherry stem.
Continuity mistake: When Frank walks up to the plane the nose is facing left. When the pilot gets on and closes the door and window the plane is favoring more center on the tower.
Audio problem: When everyone crowds around the TV set to hear the CBS News Bulletin about the Kennedy assassination, we see the TV screen with the flash bulletin card. Then we hear a Folgers coffee commercial, but the TV still is showing the bulletin card.
Other mistake: Russ pours olive oil on a salad, says it is the best vinegar, and after the next cut he grabs the olive oil again.
Continuity mistake: After Don Rickles jokes about the Italians, Crazy Joe raises slightly and shouts at him. From the opposite angle he is standing up.
