The way disputing flags is handled is rather confusing for anyone not familiar with the arcane details of the SE platform in this area. In some parts the feedback users get is only confusing, in others it is plain wrong. The main problems of the whole mechanism are
The "disputed" status of a flag only means that a single 10k+ user disagreed with the flag, it completely ignores what happened with the flagged post, what other 10k+ users think and what a moderator thought about the flag. This is very confusing for users checking their flag feedback, especially when a valid flag that was acted upon is disputed by one user.
The user that disputed the flag gets the same mod feedback as the user that flagged. As those two users obviously disagreed, one user will always get the wrong feedback. (Am I using the "Invalid Flag" flag wrongly?)
The terminology is confusing, it is not immediately obvious to users what the difference between a declined flag and a disputed flag is.
Some ideas to fix these problems:
The user that cast the flag that was disputed by another user should never see the dispution in his flag feedback. The important feedback is what a moderator did (acting on the flag or invalidating it), or what the community did with the flagged post.
Dispution should not affect the flag weight of the target flag, it should only be a way to indicate to 10k+ users and mods that the flag might be wrong, it should not have any actual affect on anything else