I'm trying to replace my slip-on spout, but I can't seem to find what to unscrew underneath because there appears to be a significant amount of rust. While I certainly hope it doesn't mean that I'm stuck with a leaky spout, I'm kind of at an impasse and was wondering if anybody had any suggestions.

Spray the area with WD-40 to clear away some of the rust5 and take a Allen Set Screw Wrench and loosen the clamp. See if you can twist the spout so the clamp looks upward. Keep trying! It'll come off, I guarantee! Cheers, Tom

Sometimes you are able to grab it well and pull on it , straight away from the wall. If not, clean rust and look for small set screw, usually from the bottom of the spout, close to the wall...