I was first suspicious of the notion of a Plato Code, as the name itself reminds one of the discredit Bible Code, but Kennedy proposes something more down-to-earth, namely that Plato used Pythagorean musical principles in the organization of his dialogues. Three main claims stand out: (i) that dialogues have an internal organization in which high points are placed in 1/12ths, corresponding to notes of a musical scale, (ii) that positive and negative turns of the dialogue correspond to consonant intervals of the scale, and this may allow us to discover what Plato "really thought" in open-ended dialogues, and (iii) that different dialogues have a different length of their 1/12th unit, which stretch from 100 lines for the Apology to 1000 lines for the Republic and 1200 lines for the Laws. Kennedy makes several interesting observations on his material, including an apparent lack of this mathematical structure in some of the Platonica that are universally acknowledged to be spurious.
Is it plausible that Plato went into all this trouble? Kennedy cites some pieces of evidence in favor of his Platonic stichometry thesis. In my opinion, the thesis is plausible: the "secret structure" may sound like a conspiracy theory, yet Plato himself (in the 7th epistle) argued against revealing the highest doctrines to the polloi, and (in the Republic) proposed that the advanced study of geometry and astronomy should be revealed -after preparation- to the guardian class. The idea that Plato had a secret mathematical doctrine, discussed only within the walls of the Academy, also finds support in Aristotle, who recounts the tale of Plato's Lecture on the Good, which ended in disaster when Plato attempted to present his geometrical arguments about the One to a lay audience. And, the relationship between the world created by the demiurge, music, and mathematical proportion is famously presented in the Timaeus.
Could it be that as the Timaean demiurge looked at the eternal model of number and proportion to fashion the universe as an expression of a musical scale, so did Plato, as the demiurge of his philosophical universe? It is an intriguing idea.
Even though Kennedy's thesis does not sound like a simple case of quackery, and circumstantial evidence lends it a level of initial credibility, the main weakness of the paper is its lack of statistical elaboration, and its reliance on expert judgments.
Perhaps there is evidence that key themes coincide with 1/12ths, but how many key themes are placed in-between notes? A thorough breakdown of the dialogues based on who is speaking, the topic of discussion, the tone, etc. would allow us to better appreciate whether or not the proposed structure actually exists.