I am a web developer and would like to debug a webapp/website on a Windows Phone device. It would be neat to have some kind of window where I can see the javascript console.
My recommendation is to test the website against desktop IE10 with all JavaScript/DOM debugging support you got there - it's 99% similar to IE10 in Windows Phone 8. For additional testing on phone you can install the Windows Phone 8 SDK and launch the website on the emulator.
Edit: nice article How to debug Windows Phone HTML5 Apps using Node.js.