The guys behind Unique Blog Designs released a great plugin a few months ago called Highlighter. The plugin allows readers to highlight any part of an article and share it via email, Twitter or Facebook. It also lets readers comment about the specific part of the article they highlighted.
It is incredibly easy to use. Once installed, you simply highlight the text you want and a box will appear which allows you to comment or share the text with others.
Commenting works really well. It allows multiple discussions to arise around your article and users can subscribe to updates in the pop up box too.
The video below shows you the plugin in action:
I love the sharing aspect of the plugin though I must admit I like the traditional way of commenting through WordPress. My only criticism is that you need to sign up in order to use the plugin (though you can later opt out of the newsletter they sign you up for).
More information about the plugin can be found at the links below 
Kevin
Highlighter WordPress Plugin: Information | Download
Sounds like a good idea in practice, but I suppose the challenge will come in letting your readers know that you have the plugin and what it does. From what I've read, it sounds like there is no interface until the reader highlights some text?
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