Q:

My flags are disputed, but flagged posts are deleted

6 of my "not an answer" flags were disputed over the night, but the flagged answers are gone.
I'll post some links. Maybe somebody with 10k+ rep can confirm that the answers are deleted:

Problem with Facebook apprequests
jQuery error in Internet Explorer
https://stackoverflow.com/questions/6486115/data-post-via-xajax-php-library/6637070#6637070

Why were my flags disputed, but the flagged answers deleted?

A:

I won't speak to your specific situation, but this does bring up an issue.
On some posts, there will be two contradictory flags:

"blahblablabla" - OP
flagging as not an answer -- NotTheOp 8/4/2012
flagging because another individual is insulting me in the comments here. can you do something? -- OP 8/4/2012

As a moderator, there are situations where one flag is correct and one flag is incorrect, but my options are to 'accept' the flags or 'decline' them. I don't have the capability to reject one flag and accept the other, leading to a state where I may decline flags even though in reality, I'm taking action based on one of those flags.

A:

A disputed flag is a flag that a user who is not a moderator marked as invalid. It means the user when to the page showing the flagged posts (except the ones for which a custom reason has been entered), clicked on "flag or disagree…" and then on "invalid flag" in the next dialog box.

When that happens, the flag is marked as disputed; nothing can be done to change that status. Even when the post is deleted, or a moderator marks the flag as useful, the flag is still counted as disputed.
To notice that disputed is different from declined; declined means a moderator declined your flag, while disputed means a user who is not a moderator marked your flag as invalid. The summary of your flags shows those separately.

A:

My understanding of this is as follows:
You misflagged them as not-an-answer, so some users will dispute them. It's enough for one user to mark the flag as invalid and then nobody wins or loses - everyone will see it as disputed rather than declined or helpful.
All of these bad answers should have gone through the natural process of downvotes and then inevitable removal from the Poster/Moderators/Trusted users. If this natural process isn't happening, then you can use the other flag and explain why the answer should be removed.
The not-an-answer flag's description can be confusing, see Should the not-an-answer flag description be clarified?

