How historically accurate the play is is not entirely clear. Its author is Tim Blake Nelson who has an assortment of acting experience and a few credits in other positions. There is nothing which clearly contradicts the historical record, but given Socrates distrust of writing it is unclear how accurately he is being portrayed. It's not clear whether Socrates would even want a play to be written and performed about his life or to what degree Plato biases the narrative to fit his own theory of forms.
A debate between Aristotle and Plato begins the play and also sets its tone. People who are intellectually exhausted from a long day of work will have trouble keeping up with the complex ideas and debates but the emotions of the actors should be sufficient to entertain those who aren't academically inclined. There is no music - minimal props, costumes and action. Lighting and scenic effects are relatively minimal but used strategically at key points during the story.
Socrates is introduced by Alcibiades in a long speech where he lavishes praise on his virtues. Homophobic people should not see this play as there are explicit references to homosexuality. Throughout Alcibiades monologue, Socrates remains mainly silent and when he speaks he is humble.
As Socrates moves on, he becomes more philosophical. He is positioned between hero and villain, between serious and funny, and between sympathetic and annoying. The narrative structure of the play is somewhat confusing, the story shifts perspectives without giving explicit context. People without knowledge of Ancient Greece will be confused throughout the play. But that's almost appropriate, given that Socrates almost seems to be motivated by confusing people and making them less certain of themselves. Still, there are a few moments when Socrates is lucid and logical and explains himself and his philosophy clearly. One example is where he describes what shape and color are simply and concretely - though these descriptions are contradicted my modern science and mathematics.
Questions are at the heart of most interaction between characters. The audience is left to contemplate or find their own answers. I found Socrates description of his experiences in war edifying. Socrates is an example of somebody whose mental health was damaged by his experience in war. Perhaps his drive to question everything was developed from his questioning of the morality of his actions during a war he did not volunteer to fight in.
The intermission ends when the trial of Socrates begins. The second act is more tragic and somber than the first. It is structured such that the audience is in the same position as those who judged Socrates almost 2500 years ago. Unfortunately there is no opportunity to change history, the audience does not get to vote to acquit Socrates and they don't get to question him. The Athenian authorities are annoyed by Socrates possibly a good portion of the audience is as well.
After his trial, Socrates' friends visit him in jail. The criticisms of democracy offered by democracy may strike a chord with viewers upset with the current state of politics. After some end of life philosophizing Socrates attempts to justify his thoughts of suicide. By killing himself, Socrates believes he is maintaining the greatness of Athens. His friends seem resigned to his fate and only his wife seriously challenges him. Throughout the play, Socrates is able to mock and undermine his critics. None of the people who dislike Socrates are heroic. But Xanthippe's passion matches her reason as she condemns Socrates for not adequately caring for his children.
Nevertheless, the play continues - depicting Socrates’ life to the last moment. This is where Michael Stuhlbarg establishes the depth of his acting skills. He captures the emotional turmoil of death more accurately than Hollywood movies would dare to try. An uncomfortable reminder as to the brutality of history and disregard for the idea of wisdom. An idea which is discussed but never fully fleshed out.
Socrates is crazy paradoxical mess that laid framework to end polytheism in Western Society. The play ends on an optimistic note - a calming in the formerly contentious relationship between Plato and Aristotle. The relationship that astute intellectuals will note is the essential summary of Western Progress. Aristotle tutored Alexander the Great who overthrew the Persian Empire and set the stage for the expansion of Greek Culture throughout the Mediterranean and Asia.