I would argue that the film is relevant both as a historical investigation (albeit through the fictional medium of film) of the aftermath of President Lincoln's assassination and as a timeless reflection on the (un)fairness of the American justice system.
The film's first half hour focuses on the night of the assassination of Lincoln, while the rest takes on the genre of the courtroom drama to reconstruct the plot, its organization and assess the involvement of Mary Surratt in it. The main part of The Conspirator thus centers on the trial of Mary Surratt, the owner of the boarding house where the assassination was partly plotted and whose missing son John is thought by the authorities to be one of the plotters. The film debates whether Mary Surratt could have been innocent and could have not known anything about the plot. This is the most historic-specific question that the film asks. The film leaves the answer open and this strategy is instrumental in asking the second, less time-specific question: can people like Mary Surratt ever aspire to a fair trial in the face of national hysteria? Here parallels can be drawn with the post-9/11 America and the treatment of supposed terrorists in Guantanamo Bay. The creators of the film have denied this was their intention, but the story of Surratt being denied a civilian trial and judged by a military tribunal has a deep contemporary resonance.