Blackboard tends to update their software once a year, before the start of the fall term, and most of the time they seem to be a year behind the current versions of Firefox. Another problem that crops up with Blackboard is that not all schools use the latest version of the Blackboard software, many schools since 2008 have been postponing updates for the software that they use due to the economy.

Quite honestly, until Mozilla comes up with a Long Term Support version (if they do that) this situation of company's like Blackboard falling behind the curve of Firefox updates is only going to get worse.

As far as Lotus Notes goes, I wonder if your school is behind on updating that software? IIRC, I have seem mention of updates for Lotus Notes to handle remote XUL problems in 4.0+ versions, brought about by security fixes in 4.0.
https://developer.mozilla.org/en/using_remote_xul
Or you could try this extension.
https://addons.mozilla.org/en-US/firefox/addon/remote-xul-manager/

Bottom line - install Firefox Portable 3.6.22 to your hard drive to use at websites that can't handle the newer versions of Firefox.
http://portableapps.com/apps/internet/firefox_portable/localization#legacy36
And use Firefox 6.0.2 (and upcoming versions) at the more modern websites which are embracing the web technology being developed for the 2nd decade of this century.

I upgraded to Version 6.02 and Lotus notes will not even open up with version 6.02!!! I tried the add-on extension that you mentioned above but it is only applicable to version 4 and is now obsolete. Google Chrome won't work with Lotus Notes but Internet Explorer will. However, Google Chrome is lightning fast with Blackboard. Time to go back to version 3.6.22 or totally erase Firefox from my machines. I'm writing this on the portable version of Firefox 3.6.22