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.
In the game when you're out on the street, if you shoot a vehicles gas tank the vehicle will explode. In reality, if you shoot the gas tank of a vehicle, the worst that can happen is it'll get punctured, gas is flammable not explosive.
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.
Although set in the time frame of 1945-1951, the cars in the game are fitted with intermittent windscreen wipers which were not invented until 1963.
The game starts in 1945 and ends in 1951. Playboy magazine, one of the collectibles, wasn't founded until 1953.
The game is set in the 1940s and finishes in 1951. Most of the songs on the radio, like the music of Ritchie Valens and Buddy Holly, did not come out until much later in the 1950s.
The second half of the story line is set in 1951 but many of the cars seen are made after 1951. The "Smith Thunderbolt", for example, is actually a 1955 Ford Thunderbird.