This is a great point and one I agree with completely. Several years ago I taught a 300-level class called "Philosophy of Biology". In that course we spent about 1/3 of the semester on logic fallacies and bad science.
It made sense to me to not limit the fallacies to science, as I think all of us are bombarded with misleading conclusions in our daily lives, whether it be reading how doctors have proven a link between some form of cancer and some food item, or product ads, etc. The students in that class became very adept at pointing out these fallacies, and I cannot help but believe they have a distinct advantage over those who are unaware.
The amazing thing (although not surprising) was how I did not have to point out the logic fallacies in the creation movement. They just flowed naturally with the students discovering them and pointing them out. I think there is value in creating a situation where the conclusion is student-derived. I simply showed examples of fallacies, then later presented students with pseudoscientific papers (including some EvC posts).
Doctor Bashir: "Of all the stories you told me, which were true and which weren't?"
Elim Garak: "My dear Doctor, they're all true"
Doctor Bashir: "Even the lies?"
Elim Garak: "Especially the lies"