Been working with SWFAddress a lot lately on a few projects, and I'd noticed some weird artifacts appearing randomly on the screen when the address value is changed from a mouse click. Strange boxes appearing for a split second in seemingly random places, etc. After a little bit of testing it was apparent that it only happened on Macs, and was the worst in Firefox.
After some googling, I found a post on the Big Spaceship blog about the issue here - it's all explained in that post, basically a strange issue with Firefox 3 and ExternalInterface calls altering the DOM window. It's not SWFAddress' fault, but it's really apparent when you're using SWFAddress for deep-linking.
The other option is to add a slight delay in your Actionscript code, from when a button is clicked to when the SWFAddress.setValue() method is called. I did it this way, and used the Timer class and a 20ms delay, and this fixed the issue straight away.