In Virginia's "fear of flying" scene at the airport, there is an airplane hangar with a sign for "Mobil" attached to it. The "Mobil" design seen was not introduced until the late 1950s. The movie is set in the mid-1940s, and the design that would have been used at that time was Mobil's logo of a white shield with large red Pegasus (flying horse) trademark and the name "Mobilgas" in black.
After Bugsy's house has been sold to finance the Flamingo Club, he takes another look at his "screen test". He's at Virginia Hill's mansion, but he looks at the film in the projection room of his old house.
After Siegel (allegedly) murders Greenburg, and as the car containing him and Virginia Hill begins to pull away, you can see in the right rear fender the reflections of two people. One is easy to identify as a human figure, the other looks like someone is possibly hunched over.
When "selling" the concept of Las Vegas to the other mobsters, Bugsy states that "when Hoover Dam opens up", there will be power for air conditioning. The scene takes place in the mid 1940's and Hoover Dam had already been producing power since the late 1930's.
In the scene where Bugsy is viewing an outdoor patriotic rally through a basement window, all the American flags are hanging incorrectly. They are displayed with the blue fields in their upper right corners, when in fact the fields should be in the upper left corners.
Virginia shoots all the ammo in Bugsy's .45 pistol; when the last round is fired the slide should stay in the "open" position rather than the "closed" position which it stays in. --This is factually one of the most common malfunctions on a semi-automatic pistol, that the slide stop fails to correctly lock the slide back on the pistol when the magazine is empty.--
When Virginia Hill is being dragged by Ben in the "Fear of flying " scene she is wearing white shoes. When she arrives in the old casino wearing the same dress and hat, she is now wearing dark colored shoes.