It could be the plugin notification icon. I think of that as looking like a small, dark gray Lego block.

When that icon appears, it indicates the page wants to use one of your plugins, or is using one of your plugins. Click the icon for more information and buttons to grant or revoke permission.

Does that match what you see, or is it something else?

Regarding Outlook mail not signing out, does it take you to MSN (what I usually see when I sign out), or does it go right back to your Inbox, or ??

If you end up back in your Inbox, is it possible that a password manager is signing you back in? Either Firefox's built-in password manager or an add-on password manager?

Thanks. You are right, it does look more like a gray Lego. I am able to click on it when I am visiting a website and it turns out is is Adobe Flash. Just doesn't tell me that when I am on Yahoo home page. As far as Outlook, it goes right back to inbox. That is, most of the time. I evidently, I think, am being signed out though, because when I ask to open it next time I do have to enter user name and password. I did check password manager and it shows I have no saved passwords.

Firefox can be a little stubborn about refreshing a cached page. To see whether you are actually still logged in, try a reload bypassing the cache, for example, by pressing Ctrl+Shift+r instead of Ctrl+r. If you really are still logged in, hmm, the logout request might not be going through.

After another user reported not being able to sign out of Outlook.com I took a closer look at what happened during that process. The suggestion I made in that thread was to make sure Firefox wasn't blocking redirects. Maybe that will help you??

Not signing out from Microsoft Outlook E-mail page at first click