Clone master, build docs, go to http://localhost:4000/react/jsx-compiler.html
The live updating is broken when using CodeMirror.
In live_editor.js, if you change
<CodeMirrorEditor codeText={desugaredCode} readOnly={true} />
to
<div>{desugaredCode}</div>
it works as expected, so I'm guessing it's something in the CodeMirror component.
This page works fine on the live site which is running React 0.5.1. It's very possible that my dev environment is broken somehow, but I followed all the steps in the readme file.