Plato believed in deeper levels of Truth and Reality underlying the world as we know it. Because of the relative imperfection of our own world, we can not fully express or directly communicate deeper Truth. However, we have an unbreakable and inherent internal connection to it. Accordingly, Plato believes in a Socratic process of teaching via questions, where the student is guided to "remember" deeper Knowledge from inside, rather than receiving it didactically from a teacher. This is most plainly made explicit in the Meno, but it underlies all of Plato's writing (and is arguably the "mystical purpose" hinted at in your question).
Because of this, Plato has a surprisingly high tolerance for imperfect argument and errors of logic. This is because he doesn't believe argument and logic (or anything else) can be perfected solely within this world. At the same time he is deliberately using many of those same errors and imperfections to lead the reader forward, and eventually allow the reader to make the leap past what can be directly conveyed and into the deeper Truths beyond. With specific regard to fallacies of equivocation, you'll find these frequently in Plato, because he is using familiar concepts as stand-ins for unfamiliar ones. The gaps that thus open up are a marker of the difference between what he really wants to talk about and the way he is forced to talk about it.
You can see this in the structure of many of his greatest works, particularly the Republic and the Symposium, where a series of differentiated speakers offer varied arguments around a common topic or claim. We are not intended to fully accept any of the arguments, so they are all presented with discoverable flaws. (The same is true of many of Plato's most famous theories, such as the Theory of the Forms.) Like the slave boy in Meno, we are shown where each argument goes wrong, but expected to make the leap to the right answer by ourselves. As I mentioned in this recent question, this is an unusual and somewhat challenging approach, but it is also used to good effect by Kierkegaard. (You can also compare and contrast an Aristotle or a Hegel, who may be wrong, but never on purpose.)
EDIT: This is one of the core standard ways of interpreting Plato, which arguably goes back at least as far as the neo-Platonists. It revolves around the mystical side of Plato, and rests on the assumption that there are things too deep to put in words. The other major way of interpreting Plato goes back to Aristotle, emphasizes his rationality, and accordingly must account imperfections in his arguments as mistakes.NOTE: This is one of the core standard ways of interpreting Plato, which is associated with Perennialism, and arguably goes back at least as far as the neo-Platonists. It revolves around the mystical side of Plato, and rests on the assumption that there are things too deep to put in words. The other major way of interpreting Plato goes back to Aristotle, emphasizes his rationality, and accordingly must account imperfections in his arguments as mistakes.