Result is that there is not an enhancement request with Oracle: "BUG:6803891 ORACLE SSO WNA SOULD BE ENHANCED TO SUPPORT FIREFOX BROWSER".
Please support that request.
Something similar seems to be the case for Vista and IE 7, by the way (bug 6795150)
Workaround.
Change the configuration; this works on the latest Firefox:- Get to the configuration screen; type 'about:config' in the address bar
- Enter 'useragent' in the Filter box
- Change general.useragent.extra.firefox to: Firefox/3.6.2 (compatible; MSIE 6.0;)
(I had Firefox/3.6.2) - the last semi colon is needed!
Bottom line is the fact the kerberos authentication module searches for "Windows NT" and then for version >= "5". Next it looks for "MSIE", which is no longer (FF V2 and up) there.
You can take it from there, see this entry.