As a moderator on Stack Overflow, I regularly look through the review history of obvious spam that has lasted more than an hour or so on the site. I often find one or two reviewers who voted "No Action Needed" in the First Posts or Late Answers review queue, allowing that spam to pass through review. I then have to look into the review history for each user and apply manual review bans as needed.
Almost always, the reviewers that have done this have failed multiple audits and have been banned from review on several occasions. It's a time-consuming and frustrating process to go and manually evaluate and ban each of these reviewers for approving obvious spam that I or the community later found.
Therefore, I'm proposing that when a post is destroyed by the community as spam (6 spam flags or one hard moderator spam flag), any reviewer who previously voted "No Action Needed" on that spam is immediately hit with a review audit failure as if they had reviewed that post incorrectly at the time it was destroyed. For those who had failed other audits, this would automatically trigger a review ban of the appropriate duration.
This would automate the process we already follow when dealing with those who approve spam. It would only apply to cases of spam so clear that the community or a moderator had to step in and destroy (not just delete) the post, yet someone voted "No Action Needed" on. Such posts automatically become audit candidates anyway, and currently register as an audit failure if someone votes this way after they are destroyed.
I can see placing a statute of limitations on this, such as only applying to reviews in the last 30 days or so. I don't ban reviewers I find who approved spam months ago (usually because they've been banned at least once in the interim).
I believe a system like this would help to identify and limit the damage of those who are letting spam slip through review without hitting attentive reviewers.
