I am under the impression that increased participation in the review queue is, on the whole a good thing. It encourages people to feel an ownership in the community and partially responsible for the site as a whole.
On Programmers.SE, I've seen what I believe to be an uptick in flagging to close (non-audits with no votes in the close queue). I believe that to be a good thing as it indicates to me that there are at least a few on P.SE who may some day become more active participants in the site.
On the other hand, I don't often see too many new names in the "recent reviews" page. There are often new names scattered about on close votes of recent questions which suggests to me there is a population of 3+k users who don't review, but do close recent questions.
While the close queue at P.SE is completely different than the one at SO (we start wondering about it in chat when it hits 20 and occasionally motivate people to help smash the queue back to 0), I was wondering if there wasn't something that could be done to help direct everyone possible to review (or at least be aware of it - there was a comment at one point of a 10k user who wasn't aware of anything in the /review link after clicking it as a new user and not seeing anything in it that could be done by him).
Next to the review link display the number of reviews that user is capable of doing at this time, akin to the way the 10k banner looks when there are flags or edits outstanding.
Many people perceive numbers as "there is something here that needs my attention". Inbox size, alerts on mobile device apps, notifications, etc... Using this it would be possible to point people to the review part of the application and help them become a more active participant in the site and the community as a whole.
This number would be:
min(first post queue size, first post audits doable) + min(late answer queue size, late answer audits doable) + ...
There seems to be some confusion about what this would be and what the numbers on it would be.
I have used my considerable art skills (sorry, no pie) to make a mockup of what this would look like based on the current snapshot of what I see on P.SE
"Wait," you say... "why is that a 20? Shouldn't it be 24?"
Nope. Because on P.SE I can only do 20 close vote reviews a day (smaller queue or something of that nature). If you hit it with someone who hasn't reviewed most of the queue, you'll actually see that its 60. And still the answer should be 20.
min(60,20) + min(0,20) + min(0,20) + min(0,20) + min(0,20) (those are the other queues there too) is 20. And that's the number that should be shown.
This should be something that you can get to 0 every day. Making it something that is an unmanageable number makes it something people will ignore, and that's not what this is suggesting.