It seems to me that for unattended backups some form of easy access to the log history is pretty fundamental. I want to know that it's reliable and has been working every day. An alternative is to send me an email on completion - can it do that ?

Regardless of reasons (but just knowing how much data was copied is one of mine) I'd still prefer more convenient access to logfile history. Also, a single logfile summarizing basic statistics after each copy… or easier access to those stats, e.g. through AppleScript variable, to simplify rolling your own summary logfile.

I vaguely remember seeing post-completion scripts, maybe using Growl, to do it.

Yes: just install Growl (http://www.growl.info). We support that, and it can be used to send you a notification of success or failure. Those notifications can take many forms, including email, small 'notification' windows, etc.