I can see how this would become a problem, seeing as when it comes to money or rewards people can get a little out of control. The competitiveness you speak of can go both ways: It can be a good or a bad thing. In the example you gave, it turned out to be bad because people became greedy and wanted the prize. Minor offenses are still offenses though, and so I don't see what the problem with reporting them is, even if the players reported aren't punished, it lets the staff know about them and if they are continually reported they can be dealt with in the future.
On the other hand, I can see people reporting others falsely because of this contest. Though, I propose a solution. To solve this you could try making it so that the person who had the most report abuses for that month that actually were right (meaning the player reported was being abusive, hacking, etc.) and if you further required the person who submitted the Report Abuse to have no false/wrong reports for that month. What I mean is all of their report abuses were correct (all reports reported at least a minor offense). This would make competitive people more hesitant to submit reports but also willing to find actual hackers and report them.
One could argue that this would make people hesitant to report hackers, for fear of reporting a player who wasn't actually doing anything wrong. There are two solutions I can think of to solve this. You could make it so that for each contest, a player could still win even if they submitted one "wrong" report abuse. This would make players less hesitant to report but they'd also still be weary of falsely reporting players because they'd only be allowed to make one mistake that month.
As I believe it was stated somewhere earlier in this thread, the people who report hackers now do it because they want the hackers caught and enjoy the server. They probably care more about helping the servers get rid of hackers than about a contest. Not to mention lots of people who report abusers are experienced players, and many experienced players tend to already have donor. In my opinion, this contest could even be utilized to help people correctly report hackers. You could make another requirement that all of the Report Abuses must be formatted correctly or the reporter would be disqualified from the contest for that month. This could be a one time thing, a yearly thing, or a monthly thing.
I personally don't care much for this, but I can see how others would like it and so I wanted to help if at all possible. If this was to be done I'm sure it could potentially help the servers out, get more players to report hackers, and many other things. I know that when I personally report a hacker, it's kind of tiresome, seeing as I have to upload a video, figure out their IGN, make sure that I have conclusive evidence that they're hacking and I'm not mistaken, and then submit the report. I'm sure that others agree with me that it can be tiresome, and so giving an incentive like this to report players could be beneficial.
(I apologize if this is unclear or doesn't make sense, it's really early).