I think the actual hint here is a reminder that if a site misbehaves, changing the user agent can be an effective troubleshooting tool.] Usually I want to open Gmail in Chrome and URLs pointing to my development server in Firefox. There is this nifty free app called Lin Castor that enables you to register your own handler for an URL.Although it had beed designed to register your own non-standard URL schemes, it can intercept standard http and https as well.That's why I call it a workaround instead of a fix.
I'd also like to understand why this works and why the problem even exists.
Simply put, you can have multiple versions of Java in different places.
What was happening on the not-working Macs was that the jdk versions were being used, and the Juniper vpn client won't work with them.
The first thing is that you have to do some configuring of both Java and Safari to get the applet to run at all.
Once that was all done, I could log in from all my Macs, fire up the applet and establish a secure connection. I made sure that the Safari and Java preferences were set the same on each machine but still no joy.