One example I have first-hand experience with is the low-volatility anomaly. CAPM-like theories predict a roughly linear, positive-sloping relationship between risk and return.
Yet decades worth of various empirical measurements of the riskiness of assets and portfolios unequivocally demonstrates that it is a negative-sloping relationship (e.g. for your willingness to bear an additional unit of risk, you actually receive less return).
But everyone says basically the same thing. "Things are more complicated in real markets."
It would be reasonable to say that CAPM is a mathematical result, and the evidence suggests the mathematical model required for CAPM simply fails to correspond to reality. But many finance folks, especially in academia, won't admit it. For them, CAPM must also be a descriptive theory.
Two sources that illustrate what I'm talking about:
[0] Baker, Bradley, and Wurgler, "Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly" FAJ Volume 61, 2011. < http://www.cfapubs.org/doi/pdf/10.2469/faj.v67.n1.4 >
[1] Baker, Malcolm P. and Bradley, Brendan and Taliaferro, Ryan, The Low Risk Anomaly: A Decomposition into Micro and Macro Effects (September 13, 2013). Financial Analysts Journal. < http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2210003 >
*disclaimer: The authors of these two papers were my bosses in a previous role, and I wrote the code and generated the results for the second paper.