This might be related to another question I found here.
I'm using yEd 3.10 64-bit along with Java 1.7.0_09 and Ubuntu 12.04.1.
The menus are not opening as expected and experienced in other programs. When clicking "File" for example, Instead of dropping down the menu opens above. This happens when yEd is not maximized. When yEd is maximized to the full screen, the menu uses all space that's available to the top, so about 1/4 of the menu is above the point you clicked on and the rest is below.
This screenshot should better describe the problem:
I haven't tried any other Java version yet, as I don't have the time to do so at the moment.