I'm also using Firefox 3.6.2, but on OS X 10.6.2 with Moodle 1.9 (not sure which version; not sure how to check!).
I've used a number of versions of Firefox without any problem, updating them as I've gone along.
When your students talk about changing browsers, I assume they're talking about changing from Safari, the Apple browser (which, incidentally, runs rings around Firefox for speed, but isn't fully compatible with Moodle, although I believe Moodle 2.0 solves that problem - fingers crossed!).
I'd ask your students to try these steps, to begin with:
Choose "Software update ..." from the top left of their menu bar and make sure that their Macintosh operating system software is fully up to date.
In Firefox, from the Firefox/Preferences .../Advanced menu select the update tab and check to see whether Firefox is set to automatically check for updates to itself. I know some people don't like automatic access to the internet, but I've never had a problem in many years of using Firefox and suggest this option. Usually the most up-to-date stable version is the best.
If the operating system is fully up-to-date, and Firefox is the latest version, and the problem is still occurring, your students could then try:
Quit Firefox and go into the [User]/Library/Preferences folder. Move the org.mozilla.firefox.plist file to the desktop. This is to check whether there's a corrupt preferences file.
Restart Firefox, go into the Moodle and try to use the smilies.
If it still doesn't work, quit Firefox and put the org.mozilla.firefox.plist file back where it came from. That way at least your old preferences remain intact and you don't have to reset them all.
If it does happen to work – and I'll be surprised if it does, frankly, but it's always worth the old college try – then throw the old preferences file into the trash and ditch it! And smile.
If none of the above works, I've exhausted my tiny store of very non-technical wisdom. All those error codes suggest this is possibly beyond the powers of a basic fix, but you never know your luck.
OK, I've left the above suggestions there because they're not bad old chestnuts to try when basic things go wrong.
But I Googled "Error Number: -2147467259 (0x80004005)" and it seems that, as I suspected, we are talking about something a bit more technical than that.
It relates to the server settings, from what I can gather. I suggest that the technicians in charge of the server are brought into this. They, too, can Google the error string, or may even have a manual with troubleshooting for it.
Just as a for example, the following URL is for a forum thread that discusses the issue:
You'll notice that there are a number of potential problems that could be causing the error, and that it's pretty technical.
Best of luck fixing things! A Moodle without smilies is a Moodle without joy!