The Mozilla developers obviously regarded this as a serious enough problem to come out quickly with a fix, in the form of Firefox version 3.6.15 which you can read about at Pogo.com and other Java pages don't work which (in case you were unsure) explains how you go about installing the update to Firefox 3.6.15.
In an admirably rapid response the Mozilla developers have, within a day or so, already released a new version to address this Java applet support issue, see Pogo.com and other Java pages don't work (which shows how to update Firefox, in case you were unaware).
Let's hope that version 3.6.15 does fix the problem (and not cause any others, as sometimes happens with bug fixes).
RELATED TIP - TESTING WHETHER JAVA IS ENABLED IN YOUR BROWSER
Last weekend I attempted to install Windows 7 Service Pack 1 (SP1), a day or two after it came out. Instead of the smooth ride that I anticipated it turned into an unmitigated disaster. The SP1 update crashed part way through, my Windows system became unbootable, and none of my desperate attempts to recover Windows to a usable state led to success. I've described it more thoroughly in my blog, see Windows 7 SP1 upgrade went horribly wrong.
I decided to do a complete 'scratch' re-installation of Windows 7, as described in the blog. After getting Windows 7 with SP1 successfully up and running, one of the many and various things I had to install was Java.
I think you might agree that installing Java, especially on a Windows platform, still has a few rough edges. One of these, for example, is just finding out just where to get the appropriate Java Runtime Environment (JRE) from. I still find doing a Google search for it is a faster way of finding the latest JRE than navigating around the Sun/Oracle web site.
And after installing the JRE, and even though I've done it many times since when Java was released way back in the mid-1990s, I still find that getting the JRE enabled and Java applets running inside a browser can still be rather tricky -- particularly so, for some strange reason, if that browser happens to be Internet Explorer!
Sometimes even establishing whether or not Java (the JRE) is already operational in your browser of choice is not always easy to accomplish. So here's a tip.
If you want to determine whether or not Java is installed and enabled inside Internet Explorer or Firefox (or whatever browser turns you on), you could do far worse than opening Michael Horowitz's Java Tester page. Read Michael's comments and advice, then just follow your nose.
The very latest version of the JRE is Java SE 6 Update 24 and once you have installed it the Java Tester page should indicate this in the pink rectangle as:
Java Version 1.6.0_24 from Sun Microsystems Inc.