For my Intro philosophy class this term, I've been somewhat reorganizing the way we approach the Gorgias (which we start out with), so as to try to emphasize the importance of context. Reading out of context is a common problem, but I think Plato especially suffers from a failure of people to read him with sufficient regard to context. No argument in any Platonic dialogue is freestanding, for instance; every single one is addressed to a person or group of people, and this sometimes affects how we should take them. In the Gorgias, for instance, people often say that Socrates has not actually caught Gorgias in the contradiction he claims to have caught him, but if you look closely at all their middle positions, it quickly becomes clear that none of them are things Gorgias himself (who does not have citizenship rights in Athens, and is trying to sell his services as a teacher of rhetoric, the art of persuading people to do what you want them to do) can say. This is actually important for the structure of the dialogue: most of the dialogue is Socrates talking with people who are not Gorgias -- people who are either willing or capable of committing themselves to things to which Gorgias himself is too clever or too cautious to commit himself. Sometimes the context is not a who but a goal. For instance, some people make a great deal about Socrates in the Republic banishing poets from the City, but this overlooks the fact that Socrates actually makes an exception for two kinds of poetry (eulogies of virtuous people and hymns to the gods, neither of which, incidentally, are rare kinds of poetry), and that the City itself is being proposed as a solution to a very specific problem: what kind of society can you have in which people are allowed to pursue luxuries but justice is impossible, or at least as impossible as you can make it? And given the importance of poetry to Greek education, the banishing of the poets is really a banishing of educators whose educational discourses could conflict with the need of such a City for education always to teach that justice is always and above all other things necessary and valuable. To make justice impossible, you must make injustice seem utterly foreign and repulsive, and you can't do that if people are also taught that injustice is sometimes acceptable or admirable. It's not about poetry as such but about education, and to the extent it is about poetry it is not about some inconsistency between poetry and philosophy, or between poetry and justice, but about the fact that not all kinds of poetry are equally good at contributing to the life of wisdom and justice. (The connection between the way one teaches and injustice is a big issue in the Gorgias, as well.) Likewise, I think Socrates' interest in definitions is exaggerated; he actually shows little sign of caring about definitions as such. Perhaps this is not so surprising given that he rejects virtually every definition that anyone proposes to him, and the fact that Xenophon has Socrates tell Hippias that he declares what justice is by doing it, not by talking about it. Talking about definitions is a means to an end, and Socrates is often quite clear that the real lesson to be taken away is not what the definition of (say) justice is, but what you should do upon realizing that your definition of justice doesn't do it justice.
I don't talk about all of this; but I do try to emphasize the importance of context. When you find an argument in one of the Socratic dialogues, you should always ask, "Why is Socrates making this argument to this person?" and "Why is Socrates raising this argument at this point in the discussion?" Sometimes it's not very easy to tell, and sometimes the real key lies in some other question entirely, but sometimes figuring out the answers to these questions illuminates the meaning of whole sections of the dialogue.