The Scheduled Copies window (Window > Scheduled Copies) shows you if the backup has run, and the log (accessed from there) will show you what happened.
SD! will leave itself up, and turn the schedule line red, if there was an error during the copy.
You can install Growl (
http://www.growl.info) if you would like notifications on success/failure either by email or other mechanisms (including, with Prowl, notifications pushed to your iPhone).