This seems kind of obvious so you've probably already considered it, but what about simply limiting the number of times members can use the function in a given period? Those who would otherwise abuse the system might be more inclined to temper its use if they know they only have so many anonymous complaints available.
And if they don't, then they've effectively wasted them and have to go back to complaining the old-fashioned way until their "quota" is restocked at the start of the next "period" (whatever that is deemed to be). Maybe this will encourage them to be more sparing with the function and only report legitimate complaints. And I suppose repeat offenders could always be locked out ("suspended"?) from its use, couldn't they?
Eh... Like I said, I'm sure you've already considered this. It seemed like a good idea at the time, but now that I've written it down and re-read it I'm not so sure.
Well, it's just a thought. Perhaps it'll be useful.