You can definitely see the #problemsofclass happening here. Thersites, we are told, is this ugly, misshapen, horrible person. And yet… He says something that is very similar to what Achilles said. He points out the problems of Agamemnon. However, because he is of a lower class he is not allowed to and, indeed, is punished for it. You could try to make the argument that Odysseus, by punishing Thersites himself, is saving him from a worse punishment by Agamemnon, and maybe this is true, but I’m not entirely convinced of it. I think it is more likely that class distinctions were a huge deal. Odysseus is the king of Ithaca, Achilles the king of Pthia, so they get to speak out against kings. Thersites? Not so much.
Poor guy. He never shows up again (as far as I’m aware) so we never really know what happens to him. He’s played his part to remind the audience that there is this hierarchy that exists between kings and commoners, a hierarchy that should not be messed with or shame will happen.