Yes, I first learned about logical fallacies just before leaving the church. I was participating in an IRC chat channel, and though I had argued many-a-point in many-a-channel, for some reason these guys were RATIONAL.
I'd be arguing along, using my normal techniques (which seemed rational at the time), when someone would say, "Now that's a straw man argument, I won't accept it," or "Appeal to authority!" I was like what???
Worse, they would paste links to websites which refuted my "facts" as being urban ledgends, or stastitically wrong. They would back up their own points with links to their own facts.
It trained me. I found myself looking up all these fallacies, so I could call BS when ever they were misusing an accusation. I learned to look up my facts online before claiming them to be fact. (Found out a lot of them were WRONG! How embarassing!) I learned to find counter-references to the references they threw at me.
My brain re-wired. Shortly thereafter, I wasn't republican anymore, I was libertarian. (It wasn't like THESE guys were libertarians trying to convert me. I arrived at this conclusion using the research and critical thinking skills I obtained from them.) Another few months, and I wasn't Mormon anymore either.
A book I'd like to recommend is How to Lie with Statistics. This will help you understand statistics when they're quoted, and how they can be twisted to prove all kinds of points not inherent in the data.
If you want to do more reading on logical fallacies (though online is a GREAT place to start), "With Good Reason" will give you a print version.
If you're a woman, The Reasonable Woman by Wendy McElroy talks about critical thinking skills specifically for women, who have a different social experience than men.
Another great skill that I got from my Dad actually, and I'm not sure if I've ever seen this in print. It's the idea of a Reality Check. When you read or hear something, ask yourself if that sounds about right. Compare it with other information you have. For instance, when I hear a statistic about how many people die of X, I compare that to the number of people I know live in America: 300 million. When I saw an ad that said 150,000 children die each year from second hand smoke, I did some quick estimates. 300 million people, say maybe 1/3rd are children. That's 100 million. 150,000 out of 100 million seems like way too many kids to be dying of something like second hand smoke. Car accidents, I could believe. But with a number this high for an indirect inhalent that takes a couple of years to kill (you have to actually GET cancer first, then die of it), it just didn't seem right. At these rates, kids all over would be getting cancer and in 10-20 years, there wouldn't be any kids left.
This took very little effort to do in my head. I didn't have to look anything up to cast that statistic into question. Same with other things, like stories, etc. Constantly ask "why?" and "how?"
"Would somebody really do that?"
"If the planes that hit the WTC building were actually empty, what happened to all the people that turned up missing? What about their families? How does a conspiracy with that many people involved keep any secrets?"
"Why would X go to so much effort to do Y, when it would have been much easier to do X?"
The point of the reality check isn't to find the actual answer. It is to determine at quick glance if what you're hearing is within the realm of reason or believability.
The other thing I live by now is to not take a strong opinion or stance on anything unless I can defend it. If I haven't done the research to become convinced myself (research on BOTH sides), I will not argue for or against it. I might mention "I heard such and so, but I haven't confirmed it." But I disclaim that my information may be wobbly. Or I might say, "Some people strongly disagree with your position, and they claim to have evidence to back it up, even though I haven't looked into it myself."
I guess I spent too many years parroting a lot of BS, repeating stories that were flat out lies, that I never want to do that again. :) Intellectual honesty is too important to me.
Oh, one more thing (now I'm rambling). Wendy McElroy said in her book: Don't be afraid to be wrong. She points out that in our society, we talk about the winners and losers of arguments. She says if you leave an discussion/debate having LEARNED something, or corrected a wrong conception, or brought your thinking closer to Truth, then YOU are the winner, even though the other person was right.
That is a very important thing I have to remind myself. It's less important to be RIGHT, and more important to learn.
Luna