Willingham alluded to the fact that critical thinking courses depend largely on the skill of teachers. From my personal experience, some teachers are excellent critical thinkers, but a majority of them are very bad...which is why I disagree with him when he states that critical thinking should not be taught on its own. Willingham proposes that critical thinking should be taught in the context of subject matter but I just don't think we have enough qualified teachers to do this.
I quote from one of my favorite authors, Jamie Whyte:
Alas, most know next to nothing about the ways reasoning can go wrong. Schools and universities pack their minds with invaluable pieces of information--about the nitrogen cycle, the causes of World War II, iambic pentameter, and trigonometry--but leave them incapable of identifying even basic errors of logic. Which makes for a nation of suckers, unable to resist the bogus reasoning of those who want something from them, such as votes or money or devotion.
Perhaps I'm naive, but I think the problem can be alleviated by making the introductory logic course a requirement for all students. Such a course could include elements such as formal logic, inductive reasoning, or more specifically, how the scientific method is practiced. Perhaps it could even include some simple psychology so students can learn about our inherent biases in cognition, and then some statistics so they can learn about how data can elucidate the truth. Does this sound too ambitious?