I'm currently going through Fascicule 6A dedicated to SAT solving and I can tell you it is by far the best reference. I haven't found anywhere else a complete reference that builds a SAT solver from scratch while explaining why each technique is used.

Regarding more classical algorithms, I never bothered reading the other fascicles. I think there are much more practical references but none is as complete and detailed as Knuth's treatment. He goes to the bottom of any algorithm, not just proving it has the right complexity but also asking what inputs are the most difficult, what other problems it can solve, etc. In the end you understand the field much better and have a good idea of what the boundary of knowledge (ie research) looks like.

But, and I say that as an ICPC world finalist, if you just want to solve practical problems you probably won't need TAOCP.