John F. Kennedy, who is referenced in the story, was inaugurated as the 35th President of the United States on January 20, 1961, the day that this episode first aired.
The same plot would be used years later in the Jim Carrey vehicle, Liar Liar. In this case the infamous liar's profession is used car salesmen, and in Liar Liar it's lawyers.
The title refers to the oath given a witness before a trial or deposition that he will tell the "truth, the whole truth, and nothing but the truth".