Focusing on your "flagging" idea - those criteria would not make for very useful flags, and it would probably just fill the queue with the equivalent of VLQ flags. Someone clicking the same option multiple times in a row in that queue does not necessarily mean that they are a bad reviewer, and we'd be getting way too many false positives.
Instead, I'd like to see an automatic flag for users who consistently use an action opposite of the rest of the community. In the instance of the First Posts and Late Answers queues, this is not possible because a single No Aciton Needed vote will end review for that item, but hopefully it will require more reviewershopefully it will require more reviewers at some point.
If that were to be implemented, we'd then have something to compare their activity against, rather than just blindly assuming they aren't reviewing correctly. The flag could also be expanded to cover all the queues. For example:
In the First Posts and Late Answers queue, someone completing the item as Reviewed (having taken some action) would counter one or two users who had selected No Action Needed.
In the Close Votes queue, a person who chose to vote to close when three other people left it open, or one or two people opting to leave it open when three or four chose to close. The opposite could be applied to the Reopen Votes queue.
In the Low Quality Posts queue, a person saying that it Looks Good when two or more other users had already recommended deletion of the post. Also, keep track of users who said something looks good but then later got deleted by a moderator.
In the Suggested Edits queue, a person who rejects an edit that then gets approved, or a person who approves an edit that then gets rejected.
Basically, keep track of whenever a user takes the opposite action of the majority of the community. If a user consistently takes the opposite action of many other users, then generate a flag so that moderators can review their history and make sure they're using the review queues properly.
This could potentially catch some of those users who are consistently the only person to approve or reject many edits in a row, or who consistently say a low quality post looks good when it had three or four Recommend Deletion votes on it already.
This would obviously be a fairly complicated algorithm similar and would probably remain secretive similar to the post ban algorithm, but I think being notified of users who are always choosing the seemingly wrong actions would be useful in the long-run.