I am also trying to run in Explorer (version 11) and it requires me to download the GWT Developer plugin for Firefox.
To avoid that, open IE11 dev tools and under the "Emulation" menu change the "Document mode" from "Edge" to "10". The page should refresh and from there you should be able to install the GWT plugin for IE.
Once it's installed you can fall back to the "Edge" document mode.
Worked for me.
But as @apanizo said, I'd use the Super Dev Mode if possible. The dev mode is already not supported anymore in the latest firefox and it is going to be the same for the upcoming Chrome 35. No clue about IE though.