Among other things, I learned that:
the powerful type system eliminates a large class of bugs the compiler eliminates the long name spaces (and the corresponding run-time look ups)
getters/setters actually lead to better compression
you can split the client side code in multiple, independently loaded modules
the pseudoclassical pattern used for OOP is actually better than the functional pattern (when combined with the Closure compiler)
you can easily extend the Compiler with extra features...
I've been using the compiler for months, slowly adding type annotations as I went, but not really "getting" a few key concepts.
Investing in the book was worthwhile, especially since it's the only source for documentation for certain types of compiler optimizations or the module functionality.
A great combination for the front end through is CoffeeScript + the Closure compiler + jQuery (or your favorite dom library).
It's similar to json-templates but with a few extra tricks. You can find some documentation here: http://www.nitrojs.org/normal-template