I think this problem is so frustrating because it has such a variety of causes, and they don't seem to happen for everybody. A screw gets loose in the operating system and issues like the following are the result (my iPhone does not have this problem at all, but my iPad mini does). These are the two issues that I have in particular.
One well-known cause seems to be that deleted music and videos, instead of going away completely (although they initially appear to) come back on the next sync as "Other." A workaround for this is to use DiskAid to clear out the folder iTunes>Music or any other folders under Media that are taking up an unexpected amount of space, then re-sync. To be safe, I clear out the contents but not the folders themselves. Be careful with this.
Another is that streamed media does not go away after viewing, even with restarting the iPad and syncing it several times as I did. My workaround, again, is DiskAid and clearing out the folder "CloudAssets."
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The other well-known issues include a huge amount of email (can sometimes be fixed by syncing fewer days, if your account allows it) or other messages. iOS needs to start calling these "Mail" or "Messages" or "Voicemail" so we can grapple with the problem more easily. I have both an Exchange account and a Gmail account, and neither is the cause of my "Other" issue -- but for some people this is obviously the problem.
It also seems probable that some other miscellaneous apps get their data labeled "Other" rather than "Documents and Data" as they should be. I hypothesize that data that is mislabeled in this way does not go away when you look at your usage in the iPad's settings and try to delete data from bloated apps. I think some of it gets hidden away in obscure folders and never cleared -- a problem similar to the first two I described.
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Don't restore your iPad from a backup. Yes, the extra "Other" will disappear temporarily, but it will be right back within days. This is not a permanent fix. I think it is possible that a complete reset could fix the problem at least until that same screw gets loose again.