I think I remember reading somewhere that the Google Wave team gave up on supporting ie6 so this suggests that GWT doesn't eliminate all cross browser issues.
I don't use it though. I have looked at it and I don't see the point of compiling java to javascript. I like the output it produces but I don't like the workflow. I am not fond of java's verbosity and I would have preferred an approach similar to the one taken by YUI in implementing rich widgets in javascript.
The cross-browser promise of GWT will only get you something that runs in ie6. It might never give you something that performs well.
No layer of abstraction will ever cover up the fact that you have the world's worst garbage collection algorithm coupled with the world's slowest javascript runtime. At best, it can only make the semantics of your code the same across the various browsers.
It's the difference between getting an obese person to walk 26 miles when what you want is for them to run a marathon.
Also, at its core GWT is just the compiler, and you can (if you desire) choose to ignore the cross-browser abstractions and work at a lower level if you want the best possible performance. For example, a mobile safari app written in GWT (one that needs to fit inside a very small browser cache) might avoid using GWT Widgets to keep the resulting javascript as small as possible. It could be that the Wave developers took that route.
So far I have not encountered browser compatibility issues with GWT. Please do understand that GWT handles the JS part, someone still have to handle the CSS part.
Someone has to handle DOM part too. If you are writing your own widget wrapper (if you are subclassing UIObject or Widget, and I imagine that the Wave team is doing this), you will also have to handle cross-browser compatibility.
I don't use it though. I have looked at it and I don't see the point of compiling java to javascript. I like the output it produces but I don't like the workflow. I am not fond of java's verbosity and I would have preferred an approach similar to the one taken by YUI in implementing rich widgets in javascript.