Character Analysis
The only thing that we know or need to know about Quinn is that he fights dirty. He's not a politician, but he's a very important political operative and adviser (9). If you want a modern-day equivalent… well, actually, there are lots of political advisers who are very important and who fight dirty: pick anyone who shows up on news shows to discuss why X or Y is good for their candidate and bad for their opponent. That's Francis Quinn. Except, in Quinn's case, he would've started a rumor about X or Y in the first place.
Now, we don't actually know what Quinn supports politically; we only know that he's against Byerley because he's a reform candidate (24). Whatever it is that Quinn stands for (probably crooked deals and other bad things), we do know that Quinn is quite willing to use dirty tactics to beat Byerley. His main dirty tactic is claiming that his opponent is a robot; and he gets Susan Calvin involved in this by threatening US Robots. (This follows the trend of main characters getting involved in stories because someone else makes them. Check out the "Classic Plot Analysis" for more on that.)
But Quinn isn't dumb. He may be evil—and, actually, he's kind of dumb because his own rumor backfires and ensures that Byerley gets elected. But this is what he's not dumb about: Quinn guesses that Byerley is a robot created by the real Stephen Byerley after his car accident (221). That might be a crazy conspiracy theory or it might be the truth. Calvin seems to agree with him, so maybe Quinn got it right. And he's certainly useful in this story for telling us what may be the truth.