More about critical thinking than symbolic logic, but two excellent books (as readable as novels) that do go into some of the logical fallacies with very real examples of each are:
WHY PEOPLE BELIEVE WEIRD THINGS by Michael Shermer
(Shermer is the editor of Skeptic magazine and is basically a much nicer version of James Randi; he debunks a lot of televangelists and channelers while still seeming compassionate.)
THE DEMON HAUNTED WORLD by Carl Sagan
In my opinion, this book was as important a contribution as COSMOS. Like Shermer, Sagan delves into modern phenomena like the Satanic Panic craze and the danger of a world that’s surrounded by breathtaking scientific breakthroughs being led by people who have no scientific knowledge and cut funding for their scientific advisory board.)
Both examine fundamentalism, pseudoscience, cults, and other real examples of applied illogic.
Another book for the layman (which I am):
LOGIC AND MR. LIMBAUGH: A DITTOHEAD’S GUIDE TO FALLACIOUS REASONING by Ray Perkins. It’s out of print but available through the larger internet used bookstores or through interlibrary loan. Perkins takes more than 100 examples of logical fallacies from Limbaugh’s broadcast and explains why each is an example of poor reasoning. (I loved one of the reader reviews on Amazon.com when the book was in print: “This is arrogant and obnoxious. You can’t take just 100 or so comments by an on air personality and then use them to say he’s not good at logic!”- they weren’t being facetious.)
Try The Mathematical Experience by Davis and Hersh (Hersch?). Although it might be a bit broader than you are looking for - talks about the logical basis of mathematics, but also other topics in mathematics.
I would also second Goedel, Escher, Bach. If you can work your way through this, you’ll be in fine shape for your course.