I get some errors with updates download and need to watch logs for errors. In the google you will find many path for SCCM 2007, 2012, 2012 R2 where find PatchDownloader.log and other logs.

Where to find logs in this versions:

%WINDIR%\System32\CCM\Logs

%WINDIR%\SysWOW64\CCM\Logs

In my case they host in next folder:

C:\Program Files\SMS_CCM\Logs