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X-Men: First Class (2011) - 35 mistakes
This has been explicitly stated by the director as not being a reboot of the franchise (in this interview, and verified by a consistent cameo appearance I won't ruin for anyone who hasn't seen it yet). It's simply a prequel to the other X-men movies, and as such differences in continuity between this movie and those are valid mistakes. Please don't get too worked up over it - this is meant to just be a bit of fun, after all...
Factual error: When the US & Soviet navies attack the mutants on the beach they fire a large volley of surface to surface missiles. This is supposed to be 1962, the Cuban Missile Crisis, and ship launched surface to surface missiles had only just been introduced and weren't very common. But what makes this a technical error is that in the barrage we see RGM-84 Harpoon anti-ship missiles, introduced in 1977, and RGM-109 Tomahawk missiles (could be anti-ship or land attack) developed in the 70s and first entering service in 1983.
Factual error: A Westland Bell 47G helicopter with the a registration of G-CHOP is seen to land at the Russian army camp/military headquarters when Charles, Magneto and the X-Men are approaching. The registration denotes it is a British aircraft, so unlikely to be in the middle of Russia, and this particular model was built in 1966 - four years after the Cuban missile crisis