as GWT is supposed to abstract all the browsers implementations (for widgets, etc) is it worth doing cross-browser testing? I was just thinking to test only the styling related stuff (CSS related) in different browsers.
Any opinion on that?
Definitely test cross-browser. GWT widgets are just DOM elements, i.e. FlowPanel is a DIV. Apply your own CSS to that and it's just like any other front-end framework. In my experience IE7 is always the one that gets you. I know everyone hates on IE6 but IE7 has a lot of the same bugs, and you probably don't develop in it, so it's the one to watch.
But for the code, EMCAScript implementations are remarkably consistent cross-browser. The only real differences are which methods exist, such as