Factual error: During the 4x4 chase across the island, the Land Rover used is a modern variant, not in production in 1963.
Character mistake: When Gaby's car becomes wedged between two buildings, she says, "Good plan. All we have to do is get over two twenty-foot walls and a minefield." While minimal backstory is given, I think it reasonable to assume that she has lived in what was East Germany all her life. It is thus highly unlikely that she would express a measurement in English units (being bilingual doesn't mean you automatically convert measurements). She would have said something like "six meters."
Continuity mistake: After Solo puts the bracelet he lifted from the Contessa on Victoria's wrist, he reveals to her the "Etruscan" gold chain necklace which, according to the flashback, he lifted when he "fell" against her. The actual scene, however, shows her wearing the necklace as she walks away.
Factual error: During the first car chase, when Solo asks Gabby if he can "borrow her car" that she was working on, it's a 1966 Wartburg 100. The film takes place in 1963.
Continuity mistake: When Solo first bumps into Waverly at the party, he looks over his left shoulder as he says, "I beg your pardon." Later, when they are introduced, the flashback has him looking over his right shoulder.
Factual error: At the motor racing scene when the heroes first meet the villains there is an Aston Martin DB6, which is at least 3 years ahead of the film's setting.
Other mistake: During the "escape from East Berlin" sequence, Kuryakin fires a single shot at Gaby's car. Aside from the extremely unlikely possibility of hitting anything like a tire with a handgun from more than half a block away, we see just her left rear tire deflated and shredding off the rim. For the rest of the sequence, sparks fly from both rear wheels as she and Solo avoid capture.
Other mistake: Near the end of the film, when Illya's superior asks about Dr. Teller's research, a subtitle reads "whoever hold's that disc can control the world." As, in context, it is a plural, not a possessive, "hold's" should be "holds." (01:45:10)
Other mistake: When Illya is having his briefing on Solo, he's told Solo joined the army at 18 and stayed on in Europe after the war. In character profiles during the final credits Solo's date of birth is given as 1929. That would make him 18 in 1947, after the war had already finished.
Factual error: There are Hawker Sea Hawks on the deck of the carrier. They were withdrawn from service in 1960.
Revealing mistake: When the Nazi doctor starts to torture Solo in the electric chair, he turns off all lights in the room except for a single dim light bulb over Solo's head; so, we know that the background is uniformly dark. Moments later, when Ilya comes to the rescue, a lighted control room appears behind the doctor, off to one side. After they strap the Nazi doctor into the electric chair, there is now a lighted control room directly behind the chair.
Factual error: The whole computer disc thing is extremely unrealistic. If Russia and the US only suspected Vinciguerra was behind Teller's abduction and had not infiltrated yet, how would they have any idea how the research data was stored, and how would they have an example of the media used? As for the size of the media, let's remember this was 1963. Even two years later, magnetic disc storage was still in its infancy. The most advanced computer storage drives with a capacity of 5mb were the size of a small refrigerator and weighed almost half a ton (e.g., the IBM 2311). Not exactly something you could carry around in your pocket.
Factual error: There were Willys jeeps by the West/East Berlin checkpoint in the early German scenes. Most of the action is set in Italy and the jeeps there are still Willys, not a FIAT or Alfa one to be seen.
