Some generic upgrade advice: know thy system, backup thy files, set aside a large chunk of interruption-free time to do the upgrade and do it when you will impact your users minimally. There will always be problems—trouble-free upgrade is an oxymoron.
Red Hat Linux is network oriented. For example, if you choose to install “everything” and don't have networking set up perfectly and a working name server available, sendmail and Samba (SMB) will hang the machine on startup. Don't enable these programs until you have a working network.
Before building a new kernel, it's important to first uncomment the line: INSTALL_PATH=/boot in the /usr/src/linux/Makefile. Also, the default /etc/lilo.conf file points to /boot/vmlinux.2.0.31—the need for these changes is not at all obvious to the novice user. Change it to /boot/vmlinux. While you are at it, add an entry for linux.old—it may save your life.
Get a complete listing of all your third party RPMs and programs. By now all of them have most likely been upgraded to Glibc.
There is a patch available on the Red Hat web site that makes programs linked against the old libc work correctly—get it.