Hi, I'm the developer at Biomatters who tracked this down for Geneious. Here is what I found.
It has always been the case that the Swing documentation says that all Swing methods must be called only from within the Swing thread unless the method's API doc specifically says that method is thread-safe. Up to now there have been no problems seen calling some methods that do not say "thread-safe" in the javadoc and that seem like they don't cause actions in the GUI and should be safe. In particular, it is common to not think about threads when you initialize the Swing GUI layout theme by calling UIManager.setLookAndFeel() at the very start of running an application, before you display anything.
With this update to Java 6 we have found that you must wrap the call to UIManager.setLookAndFeel to ensure it is called from within the Swing thread, just like you do with other Swing calls. Some small test programs that don't do that still seem to work, but you can no longer get away with it.
It is probably common practice to set the application's look and feel when it starts up. If you do, change that to do it in the Swing (also known as the dispatch or the GUI) thread.
There may be other Swing methods that are not documented as thread-safe which used to let you get away with that too, so check your use of Swing to ensure that you are properly using the methods that are not labeled in their JavaDoc as thread-safe.