From the Hypothesis About Us page:
Hypothesis is a new effort to implement an old idea: A conversation layer over the entire web that works everywhere, without needing implementation by any underlying site. Our team creates open source software, pushes for standards, and fosters community. Using annotation, we enable sentence-level note taking or critique on top of classroom reading, news, blogs, scientific articles, books, terms of service, ballot initiatives, legislation and more. Everything we build is guided by our principles. In particular that it be free, open, neutral, and lasting to name a few. Our efforts are based on the annotation standards for digital documents developed by the W3C Web Annotation Working Group. We are partnering broadly with developers, publishers, academic institutions, researchers, and individuals to develop a platform for the next generation of read-write web applications. You can follow our development progress on our roadmap. Many have contributed tools, plug-ins and integrations.
You can use Hypothesis on this project. Sign up for a (free!) account and you can start annotating this very passage.
Full disclosure: I am in no way affiliated with or compensated by Hypothesis. I just think it's cool.
But there are other options. I’m especially intrigued by Hypothesis, a set of open source tools that “adds a layer over top of the web,” allowing users to add sentence-level annotations to anything. Hypothesis saves these comments as a separate layer, rather than embedding them directly into a specific website. It’s like the linkbases of old, but for comments rather than just for links.
The work is intended as both an argument for and illustration of the web that could be. Beyond this screen, you'll see a very different sort of interface. You'll be able to explore based on your own interests and to add your own comments throughout. (You'll need a free Hypothesis account for that last bit.)