In the early scene where the family has breakfast there is a glass bottle of juice visible, which change amount of juice back and forth between each different camera angle, less juice, full juice, then less again, then back to full etc.
When J. Paul Getty is being interviewed by Playboy magazine, Getty is sitting opposite the interviewer and is fondling a dog that's sitting to Getty's right. When the camera switches back to the interviewer while they're still talking, we see the dog in the foreground moving around in front of Getty. When the camera switches back to Getty, without any break in the conversation, the dog magically appears once again at Getty's right-hand side.
At the very end of the film, Gail examines a head bust of J. Paul Getty. While it is partly obscured, one can tell the bust is of Kevin Spacey's version of Getty. However, on the final close-up of the bust, it is of Christopher Plummer's version.
Just after Paul is recovered, the car containing him pulls up to a tollgate that is swarming with paparazzi. From behind, you see the car pull in, stop, and the tollbooth worker takes a document from Chace, who is driving. The view switches to the front, and the car is seen pulling into the tollbooth again, and re-handing the document to the tollbooth worker.
The end of the film depicts J. Paul Getty dying at the same time Fletcher Chace and Gail Harris rescue J. Paul Getty III. In reality, the elder Getty died in 1976, three years after the kidnapping of his grandson.
In the film, Gail Harris divorces John Paul Getty Jr. in 1971. In reality, they divorced in 1964 and Getty Jr. divorced his second wife Talitha Pol in 1971.
The villa model J. Paul Getty is showing Fletcher near the end of the movie is the Getty Villa in Malibu. This villa was not based on the Villa Adriana at Tivoli, that is shown being visited by J. Paul and his grandson at the beginning and mentioned again by J. Paul to Fletcher. It was in fact a reconstruction of the Villa of the Papyri of Herculaneum. This smaller mansion was destroyed in the same eruption that destroyed Pompeii in 79 CE, and was not a imperial residence, but probably the property of a well to-do Roman patrician.
J. Paul Getty is not the wealthiest man in the history of the world, he doesn't even make the top ten. Who does actually have that honor is disputed, but certainly Genghis Khan was far wealthier than JPG, at several hundred trillion dollars.
When John puts "Time Of The Season" on the phonograph, the record label is from Capitol Records. Actually, The Zombies recorded for Columbia.
When Gail is showing Fletcher Paul's room, a poster for the movie "Lo straniero senza nome" can be seen on a wall. It's the Italian title of "High Plains Drifter" by Clint Eastwood. The movie was released in August 1973, while Paul Getty was kidnapped in July 1973. But movie promotional materials, including posters, are usually prepared and distributed months before release date.
When the boy is shooting the rock in his slingshot the car is broadside to him, even a little past when he releases the shot. The rock still manages to strike the windscreen, which is impossible from that angle.
In the opening sequence that shows J Paul Getty III walking down a street at night in Rome, some of the cars present would not be reflective of typical Italian traffic; there are two large US cars, a second generation Ford Thunderbird (1958-1960) and a mid-1960s Chrysler along with an Austin-Healey 3000 (1959-1967).
In the family flashback to 1964, the mom is putting dishes into a dishwasher from the 1990s.
When Gail and Fletcher drive past the autostrada tollgates, modern commercial vehicles are visible in the background.
When Jean Paul Getty's secretary is telling Gail on the phone that her boss is unavailable, an Apple can be seen in the background. The Apple was introduced in 1977, years after 1973.
When the song "Time of the Season" is played in the movie, it's 1964. "Time of the Season" by the Zombies was not released until 1968.
Everything looks wrong in the the 1964 San Francisco Getty family kitchen. There were no stainless steel cooker hoods back in 1964 neither fitted dish washers with buttons. The foil and film wrap cutter that is visible under the cupboards appeared in 1990s, the gray wall tiles were in fashion in the 2010s and there were no mixing taps (those with the lever) back in the early 1960s. Those first appeared in the market in the mid to late 70s. Same applies for the stainless steel fitted sink.
There were no round bubble like Plexiglas telephone booths in early 70s Italy, like the one that Cinquanta is using at the 70th minute of the film.
When J. Paul Getty III meets with his mother Gail at the Rome airport in 1971, his lips don't move when he says "I wanted to stay" and "Why did you have to ruin it?".
There's an almost-frontal shot of a glass door with Fletcher standing aside of it, his left shoulder facing the glass. For a glimpse a pair of trousers can be seen reflected in the midst of the glass.
When flying into London, the Thames can be seen out of the window. The bridges Lambeth, Westminster, Hungerford and Waterloo can be seen. But to see this stretch of the river at this angle, they would be flying roughly 'south by south east', and they would be flying away from Heathrow,