From what I've read/viewed online about using GWT, the key is to develop/debug in the Hosted Mode browser versus compiling and testing in normal browsers.
As a UI developer - the rendering engine is a key piece of the puzzle when using a custom/embedded browser.
Thus (since I can't find the info anywhere), what browser rendering engine is used by the Hosted Mode browser?
Gecko (e.g. Firefox) Trident (e.g. Internet Explorer) Webkit (e.g. Safari/Chrome)
And if known, which version of the engine? e.g. (the IE6 ver of IE), or (the 3.5.x ver of FF), etc.
GWT 2.0 should get you all fixed up. It will allow you to use each of the main browsers for debug. See this link for full details. In the past I'm pretty sure hosted mode used the native browser engine for the specific platform(safari on mac, ie on windows, mozilla on linux) but this may have changed to webkit recently.