In a bedroom scene, Julianne Moore's Sarah Palin is wearing the third jersey of the National Hockey League's Colorado Avalanche. This jersey was officially announced more than a year later on November 12, 2009 making it an anachronism for her character to be wearing it in 2008 during the Presidential campaign.
In a scene where Ed Harris' character, John McCain, is woken up in the middle of the night, it is clear that his arms are stretched out above his head. This is not possible, as due to the years of physical abuse/torture John McCain suffered as a POW, he is unable to raise both of his arms above his head.
Steve Schmidt tells Sarah Palin that, if everything goes according to plan, her Secret Service agents will be with her for the rest of her life. Vice Presidents only receive Secret Service protection for up to 6 months after leaving office.