I just installed 4.5.10 on an OpenVZ virtual machine and everything seems to be working except for the Logger.
I've searched around a bit and saw that this can happen if your crontab isn't created. I checked the Zimbra user and it has a crontab so I doubt that's it. I also ran through the steps in the thread below and didn't get real far.
[SOLVED] Logger not working
One glitch I did hit is that in post #20 it was mentioned that you needed to reset the LDAP and MySQL passwords. Unfortunately, after running through that page I ended up with pop-up "unable to connect" errors. The only way I could get rid of those was to uninstall and reinstall (so I'm now back where I started, with a clean install of 4.5.10).
Does anyone have any suggestions?