I've been experiencing a red dot on the reopen queue intermittently over the past few weeks with no items available to review. Here's a screenshot of what the behavior looks like:
This screenshot was taken a couple days ago and replicated right before this posting - I clicked on the "Reopen votes" link (decorated with the red dot) from a normal page, got to the reopen votes page with the "this queue has been cleared" message, and then clicked on the dropdown menu to show that red dot still decorating the "Reopen votes" link. I suspect somehow the red dot for the close votes queue is "leaking over", but I can't be sure.
I've done some searching on meta about odd appearances of the red dot, but the chief complaint was about review queues that people can't access which is not this issue. Nor is this a duplicate of this question about the red dot on the review icon, because my post deals with the red dot in the dropdown menu.