This is a 2003 SBS server, i wasn't sure if the first steps you suggested would apply.
So I have run the SGMON troubleshooting steps
The only difference i could see in the logs between a job that was 'successful' and a job that was 'successful with exceptions' is this:
beserver: 0x1f68 14-0429:100800:Notify Return Code:0, batch:23, index:1
beserver: 0x1f68 14-0429:100800:Notify Return Code:0, batch:23, index:2
beserver: 0x1f68 14-0429:100800:Notify Return Code:0, batch:23, index:3
These are the lines I noticed when I didn't get a notification.
I did a search for the word 'adhoc' in both logs and didn't find it in either logs.