Whenever I put something in to handle an event or act on a subset of data, I write something to let me see the opposite too - all the data that wasn't affected. That way, I get a quick sanity check that the process isn't too narrow as well as not too wide.
For more important processes, I'll also run those scripts a few times manually in the few days/weeks following go-live, once again as a sanity check. However, I don't generally schedule the scripts to email me. I do, however, have a few key jobs that'll naturally send out warning emails on failure, but I suspect most of us do that.
Semper in excretia, sumus solum profundum variat