At Google I/O 2011: Chrome Dev Tools Reloaded, Paul Irish and Pavel Feldman introduced new remote debugging feature — which was in passing included into webkit.
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Currently no mobile browser is implementing the webkit remote debugging protocol. (Maybe you can get custom builds for android that support it)
However there is weinre, which is giving you a remote version of the web-inspector. But you have to include some code in your page in order to support it. (Because it's not a browser feature).
Weinre website
Weinre github repo