During a party scene where Dick Cheney talk to with George H. W. Bush, it is seen that Dick Cheney is taller than George H. W. Bush. In the real life George H. W. Bush is far more taller than Dick Cheney.
In the movie, all the characters including Cheney family members, pronounce the family name as "chain-y". The Cheney family has always pronounced their name as "cheen-y".
The trend to wear the American flag on the lapel didn't happen until after 09/11/2001. Bush and Cheney wearing the American flag on their lapels during the 2000 campaign is incorrect.
The film suggests that Dick Cheney got his start interning for Donald Rumsfeld first when in fact, he was an intern for Congressman William A. Steiger before joining Rumsfeld's staff.
Camille James Harman is credited as playing "Mary Matlin". The character's surname is actually spelled "Matalin".
In the middle of the movie, the Cheneys are said to raise Golden Retrievers. The two dogs shown with them are Labrador Retrievers.
The scene in which the young Dick is weaving down the road is set in 1963. The road has yellow dashed paving markings, which were not used until 1970. In 1963, the dashes would have been white.
In a scene set in 1973, Cheney can be seen lying in bed and talking to Rumsfeld on a non-Trimline telephone with a modular handset. Modular connectors were not available for telephones other than Trimlines until 1976 and weren't ubiquitous in the United States until the early-1980's.
In the Oval Office while Gerald Ford is president (mid-70s), a model can be seen of a 747 airliner with a Space Shuttle on its back. The first Space Shuttle didn't fly until 1981.