I suggest that rather then just giving an error and deleting an input people get a page that is served by Epiphany and could potentially be customized that gives the user some options:

 * Maybe suggestions for a correct domain name
 * Search for the input at Google,Yahoo,...
 * Search for input in Wikipedia,IMDB,...

I think the Epiphany browser window is huge and should be used for user interaction. And instead of going the Firefox way with the user having to add search plugins Epiphany could suggest some very common places and options for a search result. 

this may be not the GNOME HIG way but a web page isnt HIG anyway and I think handling everything in a tiny adressbar is more complicated. 

So rather do:

User does input -> Error Feedback -> Forward to a Page to suggest some options -> User selects an option.

We might also link this to cached searches or desktop-search,beagle things.

So maybe this just means to beautify and extend the current "not found" page the user gets?