With the release of iOS 6, Apple implemented a feature called remote debugging
A client is having problems with my webapp since installing the new iOS 6 and I can\'t
Additionally, if you're BrowserSync (which u should, btw), you can use it's remote debugging feature which is accessible from the UI. It should work with Safari mobile.
There's a topic about this already: How to do remote debugging with Browser-sync?
This cool feature is powered by Weinre. Not the most pleasant debugger. But it works quite well.