LiveReload works with iOS devices out of the box if you add a correct SCRIPT tag (there are no browser extensions on mobile devices).
When your site is running on your local computer (i.e. on the same one that runs LiveReload app), the default script tag is fine.
When your site is running on another server (or if you're not sure which one is the case), you need to explicitly specify the IP of your local computer:
You should be all set now! Open your site on iPhone, iPod Touch, iPad or on iOS Simulator, and live reloading should work just like it does in desktop browsers.
Adobe Shadow team has a great walk-through on their blog.
Android support? It's coming soon.