I loved these books as a kid. Now that I think about it though, this isn't so much about a clever Sherlockian piecing together of clues, as it is about being able to spot inconsistencies in stories. Save for the one about the Spanish map and the museum janitor, Encyclopedia Brown solved cases because the perpetrator was a terrible liar, and usually talked too much. People who lie with too much detail eventually let something slip, or use an inaccurate detail, and that gives them away.
So remember kids: If you have to make up a story, stick to the facts, and lie by omission.