Well, the clues shouldn't be so obvious at first glance, but with a little research or understanding there should be some serious warning flags--mostly facts that aren't precisely truthful or are misleading. Those are the items that make you wonder "Why did the author include it in the puzzle?" And those are the things upon which you should focus. Of course, a doubly clever author could do the very same knowing that the reader would focus on those misleading tidbits (pun intended).
Another clue might be in the double meaning. A puzzle can have a complex structure, as you mentioned, and some words can have many meanings. This is something that I'll have to ponder.