In a comment here, Unlearning Economics says that there are some people "who consistently beat the market, which contradicts the efficient markets hypothesis." I agree. But this is not a problem for the EMH so much as for all economics.
I say this because there are, as far as I know, no 100% true laws in economics*. Economics is instead an inexact science in which any "law" has exceptions: as Jon Elster has stressed, the social sciences are about discovering mechanisms, not law-like generalizations. Even the "law" that demand curves slope down has some exceptions.
Rather than ask, "is this theory 100% true?" - a question to which the answer is usually "no" - we must ask: in what contexts is this true? And: how true is it?
As I say, the EMH is false in the context that there are some strategies, such as momentum and defensives, which do beat the market. But it is true - or at least true enough to be useful - in the context of choosing between actively and passively managed funds.
This question is a purely empirical matter, to be settled by a careful consideration of the evidence. For example, the question of whether minimum wage laws represent an exception to whether demand curves slope down is a question of fact.
I don't say this to get mainstream economics off the hook by lowering the burden of proof. What I say applies equally to heterodox theories. For example, there are flaws with the labour theory of value. Whether these flaws are great enough to offset its strengths in other contexts is, however, a much trickier question. To claim that the flaws "refute the LTV is the same sort of simple-minded dogmatism as claiming that the defensive and momentum anomalies "refute" the EMH. It misses the point that all theories can be "refuted" by some counter-examples.
The converse is also true. One of my beefs with right-wingers is their tendency to exaggerate the scope of their theories and to turn small truths into big ones. They fail to ask: how true is this? For example, Tim Worstall might be right that some regulations are bad for the poor. But whether this means a smaller state would increase equality is a trickier matter. Similarly, the claim that immigration has reduced the wages of the low-paid is true, but only slightly so. And, I suspect, trying to defend the 1% by invoking marginal product theory is silly: it's an attempt to apply a theory in a context where it doesn't fit.
In fact, it's a form of laziness. If you think a few simple ideas - Marxism, Econ 101, whatever - can explain everything, you are saving yourself the much tougher job of discovering and questioning the evidence.
But here's a twist. Not only is the mindless application of general theoretical laws lazy, so too can be an appeal to "facts." For example, Oxfam's claim that "62 people own as much as the poorest half of the world's population" looks like a slamdunk case against equality. But it's not. There must be something odd about a statistic which says that an Indian beggar with one rupee is richer than someone who's just started working at Goldman Sachs but has lots of student debt**.
Appealing to "facts" in this case is a way of ducking tougher questions: is inequality a problem? Can we do anything useful about it?
I think the answers to these questions is "yes". But they are hard ones, to which a definitive answer might never be available.
My point here is that many people - critics of mainstream economics, Econ 101ers and some lefties - are guilty of a form of autistic category error. They're looking to economics for irrefutable big facts and theories which the discipline, by the very nature of our complex social world, cannot provide. Instead, we are in a domain of partially applicable theories and ambiguous or missing evidence. The question is how we deal with this.
* "There are no lawlike generalizations" is itself a lawlike generalization. Any idiot can play pointless logic games.
** The point is that human capital must be wealth as well as financial assets.