Mr. Thompson is like Wesley Mouch times five. Like Wesley, Thompson is nondescript and boring. In fact, he never even merits a first name. This is an important key to his character – we never fully understand the man, and there may not be much there to even understand. In a way, he's the consummate product of the looters' ideology: mediocre to the extreme, he doesn't stand out or make decisive decisions.
Mr. Thompson, the Head of the State, was a man who possessed the quality of never being noticed. In any group of three, his person became indistinguishable, and when seen alone it seemed to evoke a group of its own, composed of the countless persons he resembled. The country had no clear image of what he looked like.... (188.8.131.52)
Having Thompson as the Head of the State says a lot about the state the country is in. We get more scenes with him after Galt's radio address and see that he can scarcely fathom what a person like Galt can want.
"Now, wait! Wait! Don't go to extremes. There's always a middle ground. You can't have everything. We aren't...people aren't ready for it. . . .What's the . . .? Don't sit there grinning like that!...I don't think you understand me. I'm offering you Wesley Mouch's job – and there's nothing bigger that anyone could offer you!" (184.108.40.206-5)
Mr. Thompson is both indistinguishable and unimaginative. He's the product of the looters' system: afraid of change, indecisive, and greedy. And he's clearly unable to think outside of that system when he encounters Galt.