You seem to at least have
some personal experiences/familiarity behind your criticism, unlike almost everyone in this thread. So here's a chance to substantiate your claim. Here is a paper that was recently published in the Journal of Economic Theory
https://dl.dropboxusercontent.com/u/17516137/RapidWeaverSite...This was a co-authored publication of an economist and a political scientist (at the University of Rochester). It's one of their several co-authored pieces; and it was published in a good field journal, but not a top general-interest journal. It has so far received a couple of cites from papers on the same topic. My point is, this paper is fairly "standard" for contemporary economic theory.
It also happens to use a decent amount of measure theory.
Now, I will personally venmo you $200 if you are able to find a single mistake or "abuse" of measure theoretic concepts in that paper in the following sense: a measure-theoretic theorem, definition, or proof technique was unnecessary for mathematical purposes, and you can demonstrate why that's true by writing an alternative proof, with the same generality but without such a concept.
I'm not baiting you, I'm genuinely curious to see if you or anyone else in this thread can do it, because I had taken plenty of measure theory in my PhD days, and this paper's usage of it seems perfectly on point to me. I'm also using it as an example because the authors' language is very clear and meticulous, and you shouldn't have trouble accessing that paper without knowing economic jargon.
I can also link you a few other random economics papers if you want. Alternatively, you could admit your disparagement of economists' intellectual ability, and intellectual honesty, was perhaps misplaced.