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.
My 2c: Try changing Java's look-n-feel:
java -Dswing.defaultlaf=com.sun.java.swing.plaf.gtk.GTKLookAndFeel -jar yed.jar
java -Dswing.defaultlaf=com.sun.java.swing.plaf.nimbus.NimbusLookAndFeel -jar yed.jar
Another long-shot guess would be switching to Full Screen (Ctrl+L), when the problem happens, and then back to normal again.