There are a few pet peeves I harp on here on a semi-regular basis. Let's try a few:
1. Find the empirical problem I would point out with this study by Palmer and Schloss on color preference.
2. Find the history of thought problem with this article by Don Boudreaux on Keynesianism.
3. Find the theoretical problem with this blog post by Steve Landsburg about taxes (not one I've seen DeLong or Krugman talk about... I'm somewhat amazed this post has been so controversial and I think the issues that most people have raised are fairly semantic).
Each case that I'm thinking about is an issue I've talked about on here before (although perhaps in another context).