Well I don't know what version the getDate method was written but it must have been sometime before 1.5.11. I just remember trying Beta2 in an older 1.5.x once and it didn't work until I got up to .11
EDIT: JFactory::getDate() was introduced in Joomla v1.5.2
So Harry, if you are running Joomla 1.5.3 or newer, you've got a corrupted Joomla install. Restore from a server backup or re-upload the Joomla PHP files. Many users have reported problems like this after installing a Joomla update in an unreliable way (such as via cPanel webbrowser upload or a non-SSH FTP connection).