Continuity mistake: Near the end, when the hitman walks out of the diner, the camera focuses on the car in the parking lot, cuts back to the hitman, then cuts back to the car. The problem is the shadows in the first shot of the car are about half a meter long, but a few seconds later they are two meters long. Obviously both takes of the car were taken hours apart.
Factual error: The final episode of "The Lucy-Desi Comedy Hour" when Lucy meets Ernie Kovacs, marks the finality for Lucy and Ricky Ricardo, and Fred and Ethel Mertz. By this time the shows weren't filmed before a live audience the way it's depicted in the movie. The producers of the show abandoned the live audience earlier than the final shows.
Factual error: A woman is shown receiving electroshock treatment ("ECT") in a hospital scene which took place in 1928. Although chemicals were used to induce seizures in psychiatric treatments at the time, the use of electricity for the purpose was not discovered until 1937 and not used in the United States until 1940.
Factual error: During the scene where Bruce leaves his girlfriend's parents home, it's raining. He leaves in a huff on his motorcycle and you can clearly hear the sound of screeching rubber on the pavement. Peeling out and making this sound would not have been possible in a rainstorm.
Other mistake: In the scene where Antwone is in Cmdr. Davenport's office and he is wearing the black, long sleeve shirt and tie, he has mysteriously been promoted from E-1 to E-4. He had never reached that rank anytime in the movie.
Continuity mistake: When Eddie is about to be interrogated by the Turks, he's tied up with his hat on. In the next shot his hat is off, and just as the Turk administers the truth shot he rips Eddie's hat of his head.
Other mistake: The scenery in the "I Love Lucy" on-stage scenes shows the Ricardos' apartment with a living room window. That was the apartment they moved into after Little Ricky was born. Before that, they lived in an apartment with no (visible) window in the living room.
Factual error: The phone at the Peacocks house is too modern for the time - the cord going into the handset had a clip in cord versus being attached directly to the piece.
Continuity mistake: In the scene where Matthew Broderick leaves his wife's hospital room and has to sniff out which book she picked off the shelf while he is gone, you can see that she picked a green book. But when he comes back in he takes a blue book off the shelf, as she says that that was the correct one.
Factual error: When Buddy and the musicians tour bus is towed to the Clear Lake Auditorium for the final concert before the fatal air crash, the canopy states that the concert is on the 3rd of February. The fatal accident that took Buddy, The Big Bopper and Ritchie Valens occurred at 1am on 3rd February 1959 so the canopy should have read 2nd February.
Factual error: Just after the start of the Korean War, McArthur places a map of Korea on the hood of a jeep to explain to a subordinate general his plans to invade Inchon. The map shows the boundary of North and South Korea not along the 38th parallel, which was the border at the time (1950), but along today's DMZ - not established until the Korean armistice was signed in 1953.
Factual error: The film strongly implies that John Dudley, the Duke of Northumberland, keeps his head (literally) by converting to Catholicism. In fact, he was executed well before Lady Jane Grey was.
Audio problem: In the scene where Malcolm is playing Russian Roulette, watch closely around the part when Malcolm begins to stand over the other guy with the gun pointed at his nose. You can hear Malcolm talking, but his lips aren't moving.
Revealing mistake: When FDR is getting put in the pool at warm springs for the first time, you can see see his normal legs and they have not been done over by CGI, to look as though he has suffered through polio.
Factual error: When Richard asks Art his opinion of his book, a copy of "Haymarket Scrapbook" is on a shelf. This book was first published in 1986, yet Richard's book will be published in 1981. (01:03:00)
Factual error: Towards the beginning of the film, the Cashes receive a notice about their rent. It's the 1950's and the address has a ZIP code. ZIP codes were not introduced until 1963.
Factual error: Women's stockings had seams in 1944. When people are dancing at the party in Bayfield's apartment, the backs of women's legs appear in enough shots to show that their stockings, anachronistically, are seamless.
Factual error: The scene that takes place at the Ford release of their 1971 models has two Mustangs driving to the event. The one in front is obviously a 1973.
Factual error: A concrete barrier is shown around the White House in the 1960's. This was not put into place until the 1980's.
Factual error: Anne Frank received her diary on her birthday, and started writing on it 1 month before she went into hiding. In the movie however, she is presented with the diary on the first she arrives at the hiding place.
Suggested correction: Since this movie is based on actual events and not considered a documentary, then the film-makers are allowed to change things to their liking.
While I feel like this sort-of correction could apply to certain elements of movies based on true stories like dramatized scenes (since there has to be some condensation of time and some elements boosted for drama, which can be chalked up to filmmakers changing things), I think a film based on a true story contradicting a known hard fact like this should 100% count as a mistake. Otherwise, you could just as easily argue that any factual error in any film is invalid because the filmmakers are "allowed to change it."