Looks like your mylyn install may be broken try removing the mylyn plugin and see how you get on.
When I had a similar problem, I simply uninstalled the Mylyn/Java integration. I don't use Mylyn, and although I know some people consider it to be the best thing since sliced bread, I've never found it to be anything other than a way to screw my name completion.
Note that you don't want to disable the "Java Proposals (Task-Focused)" that that error message was trying to tell you about. That'll disable name completion as well.
I was having the same issue, but my problems started when i upgrade my project from gwt 1.5 to gwt 1.7. I read your comments and i just make two changes. Increase the Xmx to -Xmx768m and unmark Java Proposals (Task-Focused) and mark just Java Proposals. It's being work fine since i did this changes. I hope it can help you.
I had the same issue on eclipse 3.5. Upgrading mylyn features resolved it
Mylyn (or its code assist) seems to be rather picky about resources in the build path.
I had the issue and it was caused by binary files which I had accidentally added to the Eclipse built path. That does not cause any compile error or warnings but causes the exception during code completion you mention in your post.
For me it works by doing prefrerences > general > keys > Restore Defaults
Dont know its crazy but thats what finally works after all the googling and trail following.
Regards, Manish