No one would be getting a badge for one or two good reports, them need to do hundreds or possibly thousands of them to be eligible for a badge, this seems like a lot of work for someone to do normally, much less when you're the one causing the trash you hope to pick up, chances of this happening I'll say is very unlikely.
This has been discussed in the past, and although unlikely to happen, it's still a real option that would not be worth the time and would most likely get spotted or found sooner or later.
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There's still a chance to report some posts twice or more by mistake. You could for example report a post on patrol, later on reach to the same thread and report it again not knowing you've already done that. The same thing could happen if you have reported a few posts from a certain user and then proceed to report his post history.
I'm not particularly worried about the accuracy, 34 bads out of 2704 is not really a problem, but it's more of a psicological punch that could easily be avoided. I don't see how it could become a problem if it only warns you about you having reported that post before (sorry if that wasn't clear enough on OP).
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When you're right, you're right. However, adding a reason to be marked as bad is a "manual" thing to do. This would be completely automatic, implying an additional of 0 units of effort from the staff; except implementing the function.