Most of my flags have been marked as "helpful" A few of them have been marked as "declined", and the help pages clearly explain that a moderator has looked at such flags and determined that they should not be acted on. But a few are marked as "disputed". I have not found many description of what this means in the help pages, or anywhere. Just what does it mean when a flag is disputed?
When asking about the Stack Exchange system, it's usually best to look first on the site dedicated to that purpose.
Simple keyword searches are often enough, for example, "disputed flag" gives this Q&A as the first result.
A disputed flag is whenever your flag was dismissed as neither helpful nor declined, or that your flag was reviewed but no conclusive action was taken. This is intended for use in cases where the validity of a flag is ambiguous.
Currently, the following scenarios result in a flag being disputed:
An active spam or "rude or abusive" flag was cleared (but not declined) by a moderator. These flags are unique in that marking them as helpful can impose lasting penalties on the post and its author, so a special mechanism is provided for borderline flags to be cleared without penalizing the author or the flagger. This can also be done retroactively on already-dismissed flags, if a moderator clears all such flags on the post (both active and dismissed flags).
A "not an answer" or "very low quality" flag was active on the post while it was being reviewed the Low Quality Posts review queue, and the final result of the review was "Looks OK".
[Some additional Stack Overflow-only causes are not applicable here and left out of quote]
Disputed flags are considered neither helpful nor declined, regardless of the action taken in response to them. They do not affect a user's daily flag count and don't count toward flag bans.
Note that in most cases, moderators cannot manually mark a flag as disputed (except in the above first case of clearing spam or "rude or abusive" flags), so borderline flags that are manually reviewed by a moderator will generally be marked helpful or declined per the moderator's discretion.
The link in the original last paragraph is also likely to be informative, if the difference specifically between declined and disputed remains unclear.