What skills do self-taught programmers commonly lack?

Data Structures, Programming Languages (http://www.cis.upenn.edu/~bcpierce/tapl/), Code-as-Data, Patterns (mostly in the guise of how pattern Y is an inferior version of feature X oh & monads are super patterns), Functional Programming, Object Composition, Recursion, Lambda Calculus, Type Systems, Category Theory

Each of the above expands and leads to its own world. As a self learner you just have to keep exploring. For example with category theory, you pick up type theory and learn how they and sets all relate. From sites like this one you learn about the importance of unit testing and version control. From lambda calculus you can rewind to Frege, unrewind to zermelo and learn about first order logic and trace a line from Haskell to Weierstrass program - taken to its absurd conclusion with Bourbaki - to rigorize Calculus (along the way you may learn of infinitesimals and the hyperreals formulation of Calculus by robinson which I found more intuitive).

After a while I realized that I was really into Artificial intelligence, Graph theory and Subjective Probability theory. The latter two, I think will be the Calculus of the future[1]. This led me through Machine Learning, more much more numerical methods and brings me to today. I don't know much about search or compilers or a great understanding of system internals but I can pick it up if it interests me or I need it.

The downside to self learning is that with no teacher everything is harder. With no teacher you can't double check your model so really understanding takes longer. There is no need to test yourself so you are in danger of jumping around without having properly learned anything.

My solution is to read voraciously to index and just work on what I want so that if I need a concept, knowing of its existence allows me to know that I should learn more on that topic. at the least I can make that connection. Revisiting is key, if you don't understand something now move on but be sure to come back later. Relate/Analogize/search for treatments that most suit you. Good with programming and learning differentiation? Then derivatives as higher order functions paired with Euler's notation makes it way easier and makes expanding to higher dimensions more straightforward. Learning hard things gets easier if you keep at it and you continually expand your base. Its all very slow going though and knowing when to Explore and Exploit your current knowledge is tricky. Till recently I leaned too much towards explore but if you want to get stuff done you need to exploit with what you got. I doubt this approach would have been viable 15 years ago. Or before Google and Wikipedia citations. Finally, I hate academic papers behind paywalls.

[1]As the corner stone of techniques. I see the concept of entropy appearing everywhere and find the idea of quantum mechanics as a complex probability theory just incredible.

Have you read anything that really knocked you on your ass in terms of practical usefulness?

There is no programming skill that a school can teach that a motivated individual cannot learn outside of school. That is one of the great joys of working in this most democratic and meritocratic of fields. Its secrets are not locked away in an ivory tower, they will reveal themselves to all who seriously seek them. The only tuition required is hard work and persistence.

That reminds me of another hacker:

"I think one of the most important guiding principles has been this: — that every moment of my waking hours has always been occupied by some train of inquiry. In far the largest number of instances the subject might be simple or even trivial, but still work of inquiry, of some kind or other, was always going on.

The difficulty consisted in adapting the work to the state of the body. The necessary training was difficult. Whenever at night I found myself sleepless, and wished to sleep, I took a subject for examination that required little mental effort, and which also had little influence on worldly affairs by its success or failure.

On the other hand, when I wanted to concentrate my whole mind upon an important subject I studied during the day all the minor accessories, and after two o'clock in the morning I found that repose which the nuisances of the London streets only allow from that hour until six in the morning."

Passages from the life of a philosopher Charles Babbage