If accelerated compositing is used, only the redirected window is drawn when the web inspector view is attached to the web view. This is not a problem of the new web inspector, it also happened before with the old one.
Created attachment 211697 [details]
Thanks for the patch. If this patch contains new public API please make sure it follows the guidelines for new WebKit2 GTK+ API. See http://trac.webkit.org/wiki/WebKitGTK/AddingNewWebKit2API
Committed r155814: <http://trac.webkit.org/changeset/155814>