I was reading an article just yesterday about efforts to build similar systems in Victorian times... pretty interesting:

http://wilsonquarterly.com/article.cfm?AID=2056

yeah, people should totally just skip the "write books" thing, and just teach/tutor instead, since then they can get paid at the time they do it. Books are useless.

Also, from now on I'm going to fly my favorite musicians over to my house and pay them for a song or two whenever I want to listen to them.

One of my math professors was fond of giving false proofs, where some very important but somewhat subtle step had been left out. He'd then make the class figure out what was wrong with it before going on with the lecture.

One of my philosophy professors employed similar tactics, presenting us with the arguments of whatever the philosopher of the day was, then asking us to come up with counterarguments, examples, and so on showing that they were (at least partially) wrong.

My brother's law professors would examine the arguments given by the judges who ruled on various cases, and then call on random people and have them explain how one might argue that the decision was incorrect.

I think similar methods can be employed in any subject - and in any case it will be a valuable exercise not just for learning to think about what's wrong with an argument, but for really understanding the topic at hand. It's all well and good to follow along with a proof that's being given on the board, but when you're actually called upon to examine it in detail, to be sure that you actually understand every step that was taken and why it was valid, you end up understanding it so much better.. And I certainly do believe that one can get better at finding the faults in arguments with practice.