user806: I now consistently have the small orange button next to "review" (which both link to the same page) pointing out "3" or "4" but no actual items waiting for me when I click on it.
The tooltip ("~4 items to review remaining") gives a hint that the algorithm behind it cannot exactly detect how many items are present - but why? Has anybody seen this same behaviour on other SE websites?

user6: This is my own answer on Skeptics to the same issue, heavily edited by Shog to add some details:

It's the number of reviews available to anyone. As of a couple weeks
  ago, anyone who has earned the moderator tools
  privilege
  is shown the total count of pending reviews in all queues rather than
  just the number of edits they can review.
You might be confused as you don't see any open reviews, the big issue
  is that the count is not personalized and ignores that you might have
  already reviewed all of the available stuff. It is also cached for
  several minutes between updates, although it will drop to reflect
  tasks completed during this time. 
While this does reduce the usefulness of the number as a simple
  indicator of what is new, it does serve as an indication of when the
  site is in trouble: if you've reviewed all available items and the
  tasks remain in review for an extended period of time, then there's a
  problem: your reviews are effectively wasted until someone else (other
  users or moderators) go through and review the pending tasks as well.
There are some discussions on Meta Stack Exchange on whether this
  could be made less annoying. 


806: <p>I now consistently have the small orange button next to "review" (which both link to the same page) pointing out "3" or "4" but no actual items waiting for me when I click on it.</p>

<p>The tooltip ("~4 items to review remaining") gives a hint that the algorithm behind it cannot exactly detect how many items are present - but why? Has anybody seen this same behaviour on other SE websites?</p>
 6: <p><a href="https://skeptics.meta.stackexchange.com/questions/2754/whats-up-with-the-number-next-to-the-review-button">This is my own answer on Skeptics to the same issue, heavily edited by Shog to add some details:</a></p>

<blockquote>
  <p>It's the number of reviews available to <em>anyone</em>. As of a couple weeks
  ago, <a href="https://meta.stackexchange.com/questions/230742/notification-for-reviews-shows-way-too-much/230802#230802">anyone who has earned the moderator tools
  privilege</a>
  is shown the total count of pending reviews in all queues rather than
  just the number of edits they can review.</p>
  
  <p>You might be confused as you don't see any open reviews, the big issue
  is that the count is not personalized and ignores that you might have
  already reviewed all of the available stuff. It is also cached for
  several minutes between updates, although it will drop to reflect
  tasks completed during this time. </p>
  
  <p>While this does reduce the usefulness of the number as a simple
  indicator of what is new, it does serve as an indication of when the
  site is in trouble: if <em>you've</em> reviewed all available items and the
  tasks remain in review for an extended period of time, then there's a
  problem: your reviews are effectively wasted until someone else (other
  users or moderators) go through and review the pending tasks as well.</p>
  
  <p>There are <a href="https://meta.stackexchange.com/questions/191638/notify-users-of-possible-reviews-on-toolbar">some discussions on Meta Stack Exchange</a> on whether this
  could be made less annoying. </p>
</blockquote>
