I'm using Firefox 31.0, which is up-to-date as of the writing of this question, on Windows 8.1, logging into SE by means of a Google Account.
This weekend the red box with the number of unread inbox messages is being 'sticky', as is the green box with the recent 'achievements'.
The inbox messages problem
The red box is showing that I have 1 unread inbox message. I go to my inbox, read the message, and the number persists. I can go to my user panel and click on the message there, or come to meta and go back to the main site, and the indicator clears, but then it reappears. Logging out and logging back in again seems to have no effect.
The achievements problem
The green box indicating changes in reputation and achievements is also persisting after I have clicked on it; furthermore, the drop-down summary given there does not agree with the reputation changes shown on the user page (e.g. I have an accepted answer which is not showing in the drop-down).
Blue indicators are working
The blue circles that show on the user's summary page, which show the number of unread messages and the reputation changes, are acting normally. If I click on the answer there, or the reputation changes, it clears the blue numerical indicators as always.
This behavior started this weekend. I haven't seen it happen before today. I should also mention that I have the Firefox add-on Stack Alert installed, which broke some weeks ago.
Clicking on the alert button gives the error.
An error has occurred. Details are below:
An error has occurred.
keyis not valid for passed
access_token, token not found..
I will disable the add-on since it isn't working.
I have removed (not just disabled) the Stack Alert add-on, logged out of Stack Exchange, and out of Google, logged back into G&FH.SE, and the green and red indicators are back in the status bar.
I find the red inbox messages indicator more concerning than the green one. Especially since Stack Alert broke and I don't have that indicator to alert me to new inbox messages, the red indicator is the one that will show someone has commented or tried to ping me from chat. It would be a shame if users quit looking at their inbox because of a false positive on the inbox indicator.