When the radio reporter talks about the British bombing a Nazi factory, he states that the British anthem is "God Save the Queen", however God Save the Queen did not become the anthem until 1952 when Queen Elizabeth II was made Queen. In 1945 it still would have been "God Save the King" as her father, King George VI was still King.
In the mission "Buzzsaw", when Vito and Joe kill The Fat Man, as he falls to the ground, it is clearly shown that his hat falls off. However, when the cut-scene ends and returns to normal game-play, the hat is still on his head.
In chapter 3, Vito gets mad that Derrek is only going to pay him $10 to load a box of crates. In 1945, when this mission takes place, minimum wage was only 40 cents an hour, so $10 to just to load some boxes into a truck would actually be very good pay.
When Vito is captured by police and sent to Sicily to fight in Operation Husky, he states he was in the 504th Parachute Infantry Regiment. This is correct as the 504th and 505th fought in this campaign (both were part of the 82nd Airborne). But if you purchase the "War Hero" DLC and put on the service dress uniform, on his left shoulder patch is the "Screaming Eagle" which was the 101st Airborne insignia. It should have been a "AA" style patch for the 82nd Airborne.