Hmmm. Now this is interesting:
Your suggestion to use another computer prompted me to use Safari on the Leopard Server itself. It worked and brought up the Add Media pop-up properly (I’ve not tested further, i.e. whether it both displays AND works properly).
The implication is that the issue is with the browser computers, not the servers, even if I did determine that Apple’s most recent update to php is 5.2.15, not the minor tweak up to 5.2.4 that the WP 3.3.1 requirements say it should have. It is evident that the php version is not the issue, because both versions of Safari were contacting the same installation of WP.
As to what could be up with Safari on my desktop, I can’t imagine, because it’s the most recent version. Also, many people have reported the same problem with the Add Media button with Exploder on Windows and FF.
I have the most recent FF, and it behaves as Safari does on my desktop, implying a problem with some support code used by BOTH Safari and FF on my desktop iMac. I believe the latter to be up to date wrt to Java, etc., so I can’t imagine why an up-to-date Snow Leopard iMac would both behave like some versions of IE on some versions of Windows, and not behave better than Safari on a Leopard Server machine.
Curiouser and curiouser, said Alice, not speaking very good English.