President Kirkman says that John Tyler, Millard Fillmore, Andrew Johnson and Chester A. Arthur all succeeded Presidents who died in office and never appointed a Vice President. However, the 25th Amendment to the US Constitution, which enables the President to appoint a Vice President when the office becomes vacant, was not passed until February 10, 1967. Consequently, there was no legal mechanism for any of those four 19th Century Presidents to appoint a Vice President even if they had wished to do so. Prior to the 25th Amendment, the only way to fill the vice presidency after it became vacant was for someone to be elected to the position in the following presidential election. None of the four Presidents in question were subsequently elected to the office in their own right.
When President Kirkman enters the hallway and addresses the character named "Kendra", he calls her "Kimble", the name of a character from the first series, instead of by her name.