Under what circumstance would a GM have an alert saying he (or she) has a private message, but no new message is visible when checked?

I think these cases are typically caused by the alert flags being borked.  If it's a one time thing (which can happen if you check rpol on multiple devices) usually just re-checking/re-reading the messages will clear the alert.

If you've checked your PMs and the alert stays listed, try clearing out your browser's cookies and logging back into rpol fresh and seeing if that does the trick.

Another possibility, if there are a lot of PMs in a game, is that you might need to scroll down the list to find the thread with the new message.  Messages are sorted according to who they are addressed to, so if the message is not addressed to the GM specifically (ie, a private thread between two players), then it will not be included in the GM's list of new messages.

If you are controlling multiple characters (for whatever reason...someone dropped out and you kept the character around, or you've got NPCs that you've created as in-game characters, etc) and someone sends a PM to one of those characters, you'll get the PM notice...but you could need to scroll down a long way to find it.

no where to scroll down to really, Face, total of about thirteen messages.

Had to click mark all as read three times, but it went away. Unsolved mysteries...

Weird...bad cookies, maybe, or a message that got deleted before it got read...

But I've never heard of either of those requiring multiple clicks on 'Mark All As Read' to clear the indicator.