Update:
This is not the best answer anymore, please follow gregers' advice.
New answer:
Use Weinre.
Old answer:
You can now use Safari for remote debugging. But it requires iOS 6.
Here is a quick translation of http://html5-mobile.de/blog/ios6-remote-debugging-web-inspector
As pointed out by Simons answer one need to turn off private browsing to make remote debugging work.
Settings > Safari > Private Browsing > OFF