District of Columbia residents did not have the right to vote in presidential elections until the 1964 election. Vice President Nixon's appeal to the butlers to vote for him in the 1960 election is strange.
When Cecil talks to Louis at the bus station, as Louis leaves for college, they walk through a motion-activated bi-part sliding door. The scene is set between 1957 and 1961. The first automatic sliding doors were invented in 1960, and were activated by stepping on a floor mat. Motion sensors were developed in the late 1980s.
During the Barack Obama campaign scenes on the porch, Cecil wears an "Organizing for America" T-shirt. "Organizing for America" was the post-inauguration Obama organization, started in 2009. During the 2008 campaign it was "Obama for America."
In the shot from the Oval Office during the Ronald Reagan Administration a desk phone is shown with a rotary dial. Push-button phones were installed in the White House during the John F. Kennedy Administration.
In the long shot of the White House dated 1957, the fence along Pennsylvania Avenue has concrete barriers. They were installed after the Beirut bombings in 1983. In a later scene, using an old film image, the barriers aren't there.
In 1957, when the White House is shown from a distance, a red Volkswagen bug drives by, with its white convertible top down. Several years later, in front of the courthouse in Tennessee, the same car is parked on the street, with the top down.
In fine dining, it is custom to set drinks from the right with your right hand, clear from the right with your right hand, and serve food from the left with your left hand. Several times throughout the film these customs were neglected, which seems strange for a staff of professional servers to do.