A simple suggestion...
This would hopefully let a user know when he or she is out-of-line, even before any moderators notice:
Simply send the offending user a private message any time they get reported for anything.
Don't include the name of the reporter in the message (to protect the reporter's privacy), but do include what category(ies) of offense he was reported for. And, if it was a post or topic being reported, include a link to that topic/post.
It would only require a little addition to the reporting system, and it might stop some users from repeating their mistakes during the time it would take for a moderator to process the report. Some might even self-moderate -- going back to fix what they did wrong before any moderators need to get involved.
(If it becomes needed, add an option to opt-out of these messages in the user's profile, in case some users become overwhelmed with frivolous report warnings. I don't think that would happen though, because every frivolous report will be noticed by mods, and if it gets excessive, the mods can warn/punish the report-spammer.)
I would have thought this would be something that Moderators should be doing? As far as I can see most of the more serious oversights are by newbies. Perhaps there should be a Moderator/s assigned to check through Newbies, maybe put them in a type of "creche" database, to be monitored for "x" months? Or maybe the new postings could be electronically monitored.