I was getting a White Screen instead of the Custom System Messages in all circumstances where I would expect an error. Triggering the error with some debugging enabled, I saw this:
Fatal error: Maximum execution time of 90 seconds exceeded in /path/to/system/expressionengine/core/EE_Security.php on line 185
Sometimes the error would be in the database file system/codeigniter/system/DB-driver.php instead, seemingly randomly.
I tried disabling all Extensions, and narrowed it down to Low Variables. I disabled Early Parsing of Low Variables and found that I could see the errors again, so there is something about Early Parsed Low Variables and CSM that don’t get along.
Lastly, I simplified my Error templates, removing any Early Parsed Low Variables, but left that setting enabled in the LV settings, and CSM then worked without a problem.
I found this link with a bit of Googling, but I guess it is out of date, but it could be that the problem has re-occurred.