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I would like to get up to speed on the current state of empirical work done to test the assumptions and predictions of consumer theory (think Chapters 1, 2, 3, and 6 of Mas-Colell et al.).
Can anyone recommend a good survey or provide a brief summary of what we currently know about how much empirical support there is for our primary means of modelling individual behavior?
The primary literature concerned with this type of question (at least where classical results break down) is behavioral economics. There's a great general compilation of papers put together by the Russell Sage Foundation called the "Behavioral Economics Reading List" that includes, among other things, a General Introduction section with overview papers by some of the big movers and shakers (Camerer, Kahneman, Laibson, etc.).
Many of the papers you will find through the Russell Sage paper list will be on alternative methods to classical consumer theory. If you want just the tests of assumptions/predictions, I would recommend looking through the abstracts of John Lists's papers on Testing Economic Theory. List is one of the most prolific experimentalist authors on the subject and has weighed in on most questions that other people work on in this field as well. Just reading his abstracts on that page should give you a pretty good idea of the state of the literature up through 2011 (the website isn't updated). His CV is updated, but doesn't give you the abstracts without looking up the papers individually.
Another interesting issue could be on intertemporal elasticity of substitution and risk aversion. There are lots of experimental studies that you can find easily on econbiz or in similar websites. Also some other interesting studies focus on time inconsistency. You can find some famous articles by Laibson and Hepburn.
I'll do the opposite and tell you something that we do not know a lot about: The elasticity of substitution between consumption and leisure. While many Macro models provide calibrations for that, there is no - as far as I know - proper econometric exercise based on micro data that gets to this value.
