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
Continuity mistake: In this movie, Emma Frost is seen as an adult woman [roughly around the same age as Professor X and Magneto]. But the character is also in X-Men Origins: Wolverine, set years later when Professor X and Magneto are much older, but in that movie she's younger than she is in this one. Although in Origins she is Kayla Silverfox's sister and her surname is never heard - the character was advertised and created as Emma Frost.