Ninety-Nine percent of the time, when people criticise ‘mainstream’ economics, they are in fact criticising neoclassical economics. I recently came across a paper titled “The turn in economics: neoclassical dominance to mainstream pluralism?” published in the Journal of Institutional Economics, which investigates the question ” why neoclassical economics no longer dominates mainstream economics.” Note that this paper was written in 2006, before the financial crisis. The paper attempts to explain trends in economic research over the last two decades including fields such as “game theory, experimental economics, behavioral economics, evolutionary economics, neuroeconomics, and non-linear complexity theory” and explores a few possible theories as to why neoclassical economics may no longer dominate the mainstream, concluding that “non-neoclassical development at the economics research frontier provides evidence that neoclassical dominance of economics is being supplanted by a new mainstream pluralism.” If you’re interested in this sort of stuff, I recommend you take a look at the paper, although I should warn you that it is a bit of a dry read.
In general I’d agree with the conclusion, at least with regards to the research frontier. A large chunk of modern economics does not resemble the caricatures of conventional neoclassical economics at all. First of all, I’d argue a huge amount of economics is largely just empirical work, much of it using minimal assumptions or just completely atheoretical in general. The state of empirical economics in most sub-fields is actually very good [pdf]. As for macroeconomics, while the empirical quality of new papers has not quite caught up with its microeconometric or experimental counterparts, recent trends in VAR modelling has seen a resurgence in macroeconometrics which is not bogged down in too many assumptions.
And on the theory side as well there are many trends which depart from the simplistic stereotype of neoclassical economics. Even considering models with strictly rational behaviour, modern micro almost entirely consists now of evaluating things like information asymmetry (which implies bounded rationality), moral hazard and adverse selection, giving very plausible insights as to how markets or institutions may fail even in ideal situations which would surely be invaluable to many policy makers. Further still, the literature on behavioural economics or other deviations from stricly rational markets has exploded as Chris Dillow notes, with books from Nobel prize winning economists like Animal Spirits receiving much acclaim from their colleagues.
As for instruction, I certainly agree that undergraduate core textbooks could do with a clean-up. But I think students gain most of their insights from optional/supplementary modules or from additional material given to students by their professors, in this regard core macro or micro textbooks are anything but a comprehensive coverage of economics education. In my MSc course, for instance, the most popular courses students attended were modules such as experimental economics, micro-econometrics, economic history and developmental economics. It is perfectly possible, and in fact quite likely, that the majority of classes a 4th/post-graduate MSc student will take are not neoclassical in nature, at least in my university.