Violet refers to how William Randolph Hearst cannot acknowledge her as his daughter because of his wife. Hearst was not married until almost a decade after the events of the series.
Cornelius Vanderbilt is portrayed as an elderly man, played by an actor in his 70s. In reality, Vanderbilt was middle aged at the time the series is set.
Dr. Markoe takes the lead in accusing Dr. Kreizler of malpractice. But at that point, Libby had already been identified as the kidnapper, so how could Markoe's authority NOT be reduced by revelation of the fact that he had employed her?