Paul Krugman, an economist who actually does understand special relativity [pdf], points us to an old post by David Levine:
I feel a little like a physicist at the cocktail party being assured that everything is relative. That isn't what the theory of relativity says: it says that velocity is relative. Acceleration is most definitely not. So were you to come forward with the puzzling discovery that acceleration is not relative...
I don't quite get why economists think the experience of physicists is more relatable than e.g. their own. Let me think of a way to make my point to the readers of Huffington Post using an example they'd be more familiar with ... how about ... a physicist.
Anyway, the principle of relativity is actually a more general principle that the laws of physics are unchanged if observed in reference frames that have a relative velocity to one another. So strike one.
I also think Levine is using the English phrase "X is relative" in the philosophical sense of e.g. moral relativism. X is wrong (or big or small, etc) only relative to something else; there is not some absolute scale by which to measure X. Special relativity actually says the exact opposite: all velocities can be compared with the speed of light and are less than or equal to it. Velocity isn't relative, it is absolute -- compared with the speed of light. So there's strike two.
Brad Delong points out the flaw that accelerated frames are incorporated in general relativity. That would be strike three.
However, let me take a somewhat more charitable view of Levine's statement in order to get at something deeper. He is using it as an analogy for rational expectations -- and instead someone is coming forward and saying that the inability to predict financial crises disproves the EMH. Levine is saying unpredictability is actually a prediction of the theory.
Rational expectations and the EMH aren't being used as intellectual constructs to arrive at the truth here. They are being deployed in a manner similar to creationist "intelligent design". In that case, complicated systems are put forward for which there is no theory as to how they evolved as proof that evolution isn't real. A flagellum is so complicated , there is no way it could have evolved!
One's personal failure of imagination is never evidence for or against any theory.
The fact that mainstream economics can't predict financial crises isn't evidence for the EMH. We don't know the fundamental theory of economics yet. Maybe you can predict financial crises. We don't know.
In quantum mechanics, outcomes of measurements are random. That observation is not the evidence for quantum mechanics. The evidence for quantum mechanics are the precise predictions for things that are not random ... and that success is the reason we accept the randomness in quantum mechanics.
 This example is particularly funny because there is a pretty convincing evolutionary pathway for a flagellum.