I can't see anything other than topics, but I can provide opinions on those...

All of the topics in 1-4 are, in fact, important for real world usage. Dates and Times/Math are kind of specific, you won't always need them, but you should still understand them.

For section 5, Dom manipulation, you should understand this in the same way you understand how to do algebra without a calculator. In this case, your "calculator" is jQuery which is a superior way to do DOM manipulation and what you'll probably end up using most of the time. You should understand the "native" ways of doing things in order to understand what is actually happening behind the scenes, which can be useful for debugging, and for the cases when using jQuery might be overkill.

The web API section is fairly specific. You should probably understand it, but whether you need it depends on the project. Some projects live and die by these methods, others will have zero use for them.

The advanced section is important in that you need to know the concepts exist, especially ajax. Like DOM manipulation, though, ajax is conceptually important to understand, but you'll likely never use it in native form. Backbone, Angular, jQuery and many, many others have their own implementations which simplify/streamline the usage of ajax considerably.

I hate regular expressions. I suppose you need to understand them, as they're powerful. But they're also the most counter-intuitive part of programming. To boot, like most of JS, there can be slightly different interpretation/support for regular expressions. Frankly, I rip most regular expressions since most useful ones have already been poured over and corrected and tweaked to work well.

Patterns, objects, closures, etc are important if you plan to build code which others can build on, or build something which handles reasonable complexity. JavaScript is only technically an OOP language, though. The fact that its not strictly typed makes advanced OOP concepts slightly less important than, say, learning .Net or Java or even PHP. Learn it if you plan on being a front-end developer, but don't let those concepts hold you back from proceeding down the JS path.