Firefox 3 Release Candidate installs and runs fine on CentOS 5 (a community build of Red Hat Enterprise Linux 5). However, this is what I found when trying to install Firefox 3 RC under CentOS 4 (RHEL4). The first problem I ran into was Firefox 3 RC complaining it could not find the Pango Cairo libraries. So, I used Yumex to install it and its dependencies. Then, I created symbolic links from /usr/evolution28/lib to /usr/lib. The next issue is a bit more of a problem though. Firefox 3 also wants GTK 2.10 or newer. However, the latest GTK available for CentOS 4 (as far as I can tell) is 2.4. Installing GTK and its dependencies from source code can be a hassle (or it was the last time I did it a few years ago). At that point I decided it was a good idea to move the last of my CentOS 4 systems to CentOS 5 :-)
But, if this is not an option for you, be prepared to either stay with 18.104.22.168 or take on the task of installing GTK 2.12.9 (the current release).