I've edited this: I was a bit too quick. I have realised the menu error I have described below only occurs in full-screen mode. I'm not quite sure what causes the error now, as I've discovered it does actually occur both with JDK-6u30 and JDK-7u2
I'm using Ubuntu 10.11 with Gnome-shell, yEd-3.8 and (Oracle) Java 7 update 2 JDK. Under Java 7, the menus in yEd fail to work using the mouse. If I use the keyboard shortcuts, however, they seem to work alright.
If I revert to the (Oracle) JDK-6u30 things work as expected.