source: Addy Osmani https://plus.google.com/u/0/115133653231679625609/posts/Px3bQdQ2HDu
The landscape for remote debugging your apps on mobile is quite strong at the moment.
Chrome for Android supports remote debugging via USB and allows you to debug using the Chrome Developer Tools. (See: https://developers.google.com/chrome/mobile/docs/debugging and Chrome for Android Remote Debugging for +Boris Smus's video walkthrough)
Opera has had support for remote debugging since 2008 and Dragonfly can remotely connect to Opera Mobile. (Tut: http://www.codegeek.net/blog/2012/mobile-debugging-with-opera-dragonfly/)
Firefox for Android has had support for remote debugging since July and introduced support for this in Firefox 15. (Tut: https://hacks.mozilla.org/2012/08/remote-debugging-on-firefox-for-android/)
Safari on iOS6 includes an official Remote Web Inspector which will work with Macs. You'll have to use Safari 6 for Desktop to get it working, but there's a good tutorial available on this as well http://www.mobilexweb.com/blog/iphone-5-ios-6-html5-developers.
There are also tons of great apps that can help with remote debugging, such as +Remy Sharp's jsconsole.com or Weinre.
For a run-down on remote debugging and some more of your options, you might like to checkout Ryan Seddons excellent talk on the subject http://thecssninja.com/talks/remote_debugging/