I think at this point the burden of proof is on economists to justify their profession. They completely failed to foresee the recent financial crisis, with the so-called "Great Moderation" and economists like Ben Bernanke saying the depression problem has been solved.
* Theory of competitive advantage is flawed and doesn't hold up to reality. Free trade is not unequivocally good. I wrote about it in this comment https://news.ycombinator.com/item?id=15159057 , but I'm basically parroting economist Ha Joon Chang who wrote multiple books about this
* The assumption of individuals being rational and utility-maximizing is false (eg. charity, stock market).
* Efficient market hypothesis. See any financial asset bubble.
* Austerity economics. The severity of the Great Depression was exacerbated by the government's austerity response. Yet here we are 80 years later demanding austerity from Greece and such.
* Money multiplier http://positivemoney.org/how-money-works/advanced/the-money-...
* Phillips Curve
Steve Keen wrote a book called "Debunking Economics" that explains theoretical flaws in the basic supply/demand curves that are the foundation of economics, though I'll admit I didn't read the book.
Ultimately though, neoclassical economics is just too damn oversimplified to result in many meaningful actionable policy takeaways. It's too constrained by its owned rigid model of how economies are supposed to work, and thus too free market dependent and status-quo preserving.