I haven't figured out the cause of it yet but I don't think it is really machine related. I have tested this on several machines, three on Vista, one on Windows Server 2003, and two on XP. Out of those, the only one running IE6 is one of the XP machines, the rest are running IE7. One thing I noticed was that in the page source there is a script resources that shows up twice in the page source with minimal differences between the two, have no idea if that has anything to do with it.
It is a combination of certain modules on the pages -- modules that have javascript interracting with the page. I know that if I remove any instances of the SW.DockMenu, for example, it works just fine (the modules minimize with postbacks) but the moment I introduce those it decides it wants to postback instead of use javascript to minimize/maximize. All the other browsers are ok with it, however, and using the javascript console I can't see any errors so I don't know what is going on.