If memory serves, my first mental leaps for JavaScript were:
1 - it's in the HTML, but it's making the HTML. Figuring out how to organize it for sanity, and to put it in the right place to do the right thing was key.
2 - the server delivers it but it runs on the client. The fact that the code is running inside a browser, in a location that cannot directly access the internals of the server takes some getting used to.
3 - when to use it. There's many points where JSP (or other server side dynamic page generation mechanism) or JavaScript can be used. It's important to have a feeling for when it's the right tool for the job. It's not unusual to see new JavaScript developers do everything in JavaScript. Now that they have a hammer, the whole world has been converted to nails.
4 - testing & debugging - I know there's better and better tools out there, but realizing that retesting is needed for each supported browser, and how to debug browser code in each browser is a big thing the books never seemed to teach very well.