Mac mini wont shutdown
Close all Mac OS X apps before shutting down
Try to determine if one particular app is causing the problem. Maybe one app always aborts the shutdown process. Try updating to the latest version.
Open Disk Utility. Choose the your main hard drive and click Repair Disk.
Usefully shutdown freezes are caused by incompatible or outdated drivers e.g printer, scanner software. Open OS X activity monitor. Do you see any high cpu processes or unresponsive applications that are marked red?