On the other hand classes on ethics (which illustrate how not black and white the world is) and social philosophy (which present ethical models on which to base our society) both have been invaluable.
Had I to do it over again I would have started by studying rhetoric (the art of persuasion), a larger field of study that seems (to me) more relevant.
Look at this: http://en.wikipedia.org/wiki/List_of_fallacies
I quickly looked through them and didn't find anything directly relating to symbolic logic. Most of symbolic logic was trying to understand what was at first pretty confusing notation and then trying to figure out how to represent things like sets without using Venn Diagrams.
At the end of the day I don't think you start to understand any larger truths about logic. Knowing how to write out De Morgan's law with symbols is frankly kinda useless.
Maybe it helps with mathematical thinking, but that's not relevant to most people.