When I ran the 5.0.12_GA update there was an issue with the logger during the schema update to the DB (from memory, the install.log file isn't in /tmp any more). I did some limited investigation at the time and followed some hints from a similar sounding installation problem to uninstall the logger .rpm and then re-run the installation. This got the core server up again and everything generally appears to be working fine, but the server status no longer displays in the admin GUI. I've subsequently run the 5.0.13_GA update but this doesn't change anything.
The message shown is "Server status data is not available. To see the server status, logger service must be installed."
zmcontrol status appears to show the logger working. The statistics screen in the admin GUI shows everything fine as normal (not sure if this is related).