With the previous notifications menu, I could Command-click (I have a Mac; Ctrl-click does the same thing on Windows, I believe) on a link in the menu to open a new tab in the background (Firefox 40.0.3 for Mac), as I do with any other link on a web page; the existing tab remains unchanged. Since this new style of notifications rolled out, Command-clicking on a link in the notifications menu opens a new tab in the background and also opens the same link in the current tab. This is undesirable.

This is happening as of today, with the new dual notification menu.

Another user with Firefox 40.0.3 for Windows has confirmed this on en.wp at VPT.