One very useful method of getting an overview of all the recent errors on a SEPM:
1. From SEPM browse to Monitors > Logs
2. Log type: click System
3. Log content: click Server Activity
4. Time range: click Past month
5. Click View Log
6. Click Export and Save
7. Save the log as system_report.csv
This log can provide a wealth of information about the failures within SEPM.
The log also offers useful information about:
Content updates
Replication failures
Certificate information
LiveUpdate functions
The logs mentioned by other community members, above, provifde the details about each specific failure.
Hope this helps!!!
Mick