The typical view of the dramatic character of the "late" dialogues of Plato (like the Sophist) is that they don't have any. The dialogue is a cumbersome apparatus for presenting dogmatic material. The Eleatic Stranger is supposed to be merely reciting a Platonic doctrine, and Plato's presentation of it in the form of a dialogue is merely a matter of inertia.
Yet consider the small exchange at 217d8-e3. The Stranger, on hearing Socrates’ veiled request that he proceed by means of short exchanges in his investigation, he says that he would be ashamed (αἰδώς τίς μ᾽ ἔχει) to put on an exhibition (ἐπίδειξιν ποιούμενον; like a sophist, cf. Protagoras 320c3), either by himself or with another. He understands that, if he wants Socrates’ approval, he must distinguish himself from the sophists through his pedagogical success and his concern for truth; he must treat the exchange as a real exchange, not simply an opportunity to “show off;” in short, he must prove himself a philosopher.
We are clearly warned in this exchange that however docile young Theaetetus and Socrates may at times appear to be in the conversation that follows, the dialogue is never merely “for show,” and their responses will contain important clues about the effectiveness of the Stranger’s practice of philosophy, contrary to the superficial impression of dramatic inertness which still retains its hold in scholarly interpretations of the Eleatic dialogues (cf. Frede 1996).
To be sure, one may still argued that the drama of the dialogue, in spite of this warning, still remains a cumbersome facade. After all, the Stranger, in his earlier conversation with Theodorus and the boys (Sophist 217b5-9; this happens “off camera,” so to speak, before the meeting with Socrates) is reported by Theodorus to “remember well” what he heard about sophist, statesman, and philosopher from the Eleatics, and to be willing to repeat it. But this need not imply that he is about to merely recite it mechanically, pace Zuckert (2000 p. 70); this would be, after all, an ἐπίδειξιν, an exhibition. Remembrance, at any rate, will play an important role later on in the Statesman; it designates the human relation to the divine in the myth. The Stranger’s good remembrance has to be proven in his treatment of Theaetetus and young Socrates - in his ability to help them remember what is already in them.