To begin with, our interlocutors in the outer dialogue are Terpsion and and Euclides. Both are from Megara, and both have a vested interest in Socrates--they were both present at his execution (Phaedo, 59c).
The time at which Terpsion and Euclides read the dialogue is at the death of Theatetus, and subsequently, the actual conversation took place just before the death of Socrates. Theatetus, like Socrates, has similar physical characteristics, laudable intelligence and character, and contains the same modesty with respect to knowledge and willingness to admit it in conjunction with an eagerness to learn more. Socrates clearly enjoys his conversations with Theatetus as well--his demeanor is very different from the Socrates that talks to Euthyphro outside the courthouse shortly thereafter. Moreover, both Socrates and Theatetus die courageous deaths at the hands of Athens, Socrates by Athenian grand jury, and Theatetus in fighting for Athens.
There seems to be a good deal of evidence that suggests Plato's efforts to draw our attentions to the similarities between Theatetus and Socrates, especially in light of both the outer and inner dialogues taking place at the time of their respective deaths. Thoughts?