Andrew T.,
Thank you for the response, but it turned out it was something
completely different than what I initially thought.

If anyone is looking for a solution to this, here's the short of it:
DEBUG your JavaScript code.

And with Internet Explorer, this can be really tricky, especially
trying to figure out what the issue is with their messages being less
than helpful.

Here's where my issue resolved to...

My applet uses the Netscape LiveConnect to communicate between the
JavaScript and the Java.  I had a
   setupApplet(String name, int width, int height) {...}
method in my Applet code, and then in my JavaScript, i had the
following lines:
   var theApplet = document.getElementById("theAppletName");
   if (theApplet.isActive) theApplet.setupApplet("name",
theApplet.width, theApplet.height);
or something like that.

Now, before the JRE update, it would work correctly.  After the JRE
update, it worked fine in Firefox, but in IE, it did not.  Here's the
reason(s): it turns out that in IE, the "theApplet.width" was returning
a string-version of the number, and then trying to pass in a string
where an integer should be.  IE didn't like it, and thus kicked a (not
so helpful) error.  Also, because of the Applet class being returned,
"theApplet.isActive" is not going to work as well, because it's not a
proper method call.

So, the resulting line should be:
   if (theApplet.isActive()) theApplet.setupApplet("name",
parseInt(theApplet.width), parseInt(theApplet.height));

Here's my new question: why would the call work before any JRE upgrade?

Thanks, Andy