The bad news, that there is no new debug capabilities in comparison to WP7/IE9. Please take a look on How do I debug Internet Explorer on Windows Phone 7? since we are in exactly the same situation on WP8.
What I personally use on daily basis
Debug your app in IE10 Desktop as much as possible
Weinre remote debugger. Demo video. You can use the following app based on Weinre to simplify its usage (no local setup needed) - IeMobileDebugger src or link to Store
Supports
Html traversing
Html node styles, properties, metrics
Reading console output
Executing js on device side from console (including intellisense)
Dynamic script injection - ability to debug live sites
Not supported
js breakpoints
For javascript line by line debugging use aardwolf. Demo with VS integration.
To redirect console trace to Visual Studio output and be able to use console.log("some message") for tracing
index.html:
<script type="text/javascript">
window.console = {
log: function (str) { window.external.Notify(str); }
};
// output errors to console log
window.onerror = function (e) {
console.log("window.onerror ::" + JSON.stringify(e));
};
console.log("Installed console !");
</script>
MainPage.xaml.cs
private void Browser_Loaded(object sender, RoutedEventArgs e)
{
Browser.IsScriptEnabled = true;
// Add your URL here
Browser.Navigate(new Uri(MainUri, UriKind.Relative));
Browser.ScriptNotify += (s, arg) =>
{
Debug.WriteLine(arg.Value);
};
}