It seems that my Tableau Scheduler and the Windows Server it run on don't agree what the time is. When writing this, the time on the Windows server is 11/8/12 11:07 PM (that is, current UTC) but log messages contain the following timestamp:
2012-11-09 04:06:53,621_level=FATAL_server=126.96.36.199:SQ-WIN_service=backgrounder:_pid=4124_tid=0xf8acd0_user=_session=_request=_context=_message=NativeException: com.tableausoftware.vizql.dll.DataSourceException: [ODBC Driver][Database] SQL error:*** ERROR No HOME environment variables are set on the system.
Unable to connect to the server "TCP:188.8.131.52/18650". Check that the server is running and that you have access privileges to the requested database.
Similarly, the Tasks page reports that the next run time for Every 15 Minutes tasks will occur 11/9/12 4:15 AM.
So, the Tableau Scheduler is clearly confused about what time it is. A server restart does not clear the issue.