Although the Luisa Rey/Isaac Sachs segment is announced as taking place in San Francisco in the year 1973, Sachs mentions to Luisa that his flight had been delayed by the Air Traffic Controllers' strike. That strike took place eight years later in 1981 during the Reagan administration.
On the airplane carrying Isaac Sachs in the 1973 storyline, a newspaper is seen with the visible headlines, "PROP. 13 WINS BIG" and "Younger Wins - To Force Brown". Both California Prop. 13 and the gubernatorial race between Jerry Brown and Evelle J. Younger took place in 1978. The same newspaper appears again later, used to paper over the windows of the sweatshop where Luisa Rey and Joe Napier seek refuge from Bill Smoke.
John Gardner's "Win, Lose or Die" is seen on the 1973 bookshelf of Luisa Rey during the conversation with Joe Napier. This book was first published in 1989. The same bookshelf contains The Defector by Howard Reynolds, which was published in 1987.
One of Frobisher's narrated letters near the middle of the movie says "What had happened between Vyvyan and I transcended language." It should be "between Vyvyan and me" (especially coming from an educated Englishman of the 20th century).
When the young teenage customer at Papa Song's squirts the white mayonnaise-looking condiment all over Yoona-939's back, he shoots it all up over her right shoulder, but when Yoona-939 turns around to punch him, all of the condiment is concentrated on the center of her back, it's no longer on her shoulder.
The one-way "Van Ness Ave" in the film (filmed in Glasgow) does not at all look like the real Van Ness avenue (which is a wide two-way avenue, with a center divider). Nor is the Bay Bridge visible from Van Ness Ave as it is shown at one point in the film.
When Luisa Rey is run off of the bridge, the windshield and side window begin to crack in a spider web pattern. Car windshields are made from tempered safety glass. If and when a car window would start to fail, they instantly, completely shatter in to small squares.
In the book, Luisa Rey is the reincarnation of Robert Frobisher, so her line in the Record Store about knowing the music of the "Cloud Atlas Sextet" makes sense. However, for the movie they changed the reincarnations so that was no longer the case, which means the line doesn't belong in the movie.
Near the end of the movie, Luisa Rey is holding a copy of the October 1, 1973 issue San Francisco Examiner. The article under the main (fictitious) headline ("Oil Lobbyist Arrested...") and under another headline ("FBI questions...") appear to have identical text.
The goof items below may give away important plot points.
In the Timothy Cavendish "happy ending," he is writing the screenplay for the movie based on his adventures. The typewriter text shows a phrase containing the word "labored". Being English, he would most likely spell it "laboured".
In the end, two moons are shown close to each other in the sky. One of them is full, while the other is crescent. As they are close to each other and reflect the same light sources, their phases should be the same.
There are no known habitable planets from which Earth would be visible in the night sky. However, this storyline is set hundreds of years in the future, by which time a good deal of technology may exist. The "planet" in the final scene could be an asteroid or other fairly large celestial body on which Terra-forming technology is used.
Losing communications with a remote area today would result in a rescue effort being mounted. It wouldn't make sense for the Prescients to, a full century later, have to explicitly contact the off-world colonies for help to arrive.