I recently upgraded our RT from 3.6.5 to 3.8.7, running on Fedora 8 x86_64, Perl 5.8.8, Apache 2.2.9 and MySQL 5.0.45. Things went pretty smoothly by following the embedded README, UPGRADING and UPGRADING.mysql files in the 3.8.7 tarball.
However, upon restarting apache at the end of the upgrade and accessing the web interface, I was presented with a message indicating that files in var/mason_data/obj/ could not be created.
I verified that the obj directory was owned by the apache user, that the directory mode was correct, checked for selinux issues and corrected them, but the errors persisted. I su'ed to the apache user and was able to create, rename and delete files and directories in the obj directory. These conditions are suggestive of selinux issues, but the audit log was clean. Even disabling selinux did not allow the files and directories to be created.
A web search proved mostly fruitless--a number of people have reported similar issues, but no solution was offered. However, I eventually stumbled http://tpokorra.blogspot.com/2007/12/bestpractical-rt-request-tracker-on.html. This solution is taken directly from that website. I've added it to the Wiki in the hopes of saving others several hours of Googling.
The problem was solved by executing the command
chcon -Rt httpd_sys_content_t /opt/rt3/var/mason_data/obj/
If you'd like a copy of my upgrade notes, please contact me at menchini at ncssm dot edu.