The SharePoint 2010 Timer service terminated with service-specific error %%-2147467259

Today I have been dealing with lots of errors being logged in the System event log in a SharePoint 2010 development environment.  The error is Event ID 7024:

The SharePoint 2010 Timer service terminated with service-specific error %%-2147467259

I tried restarting the Timer Service and restarting the Windows 2008 server but this didn’t stop the messages being logged.  While looking around Central Administration I could see that there were no scheduled jobs:

I couldn’t really see anything obvious in the ULS logs but after various troubleshooting steps I fixed this by adding the service account used by the SharePoint Timer Service to the local Administrators group and restarting the Timer Service.