External Apple USB keyboard, Shift+Tab and Command+Shift+Tab doesn't work I have an aluminum Apple USB keyboard plugged into my MacBook Pro (Late 2011). Command+Tab works fine to switch applications. But Command+Shift+Tab doesn’t! The same shift key works to capitalize letters, so what on earth is going on?

This is the case with both the left and right side, and combinations of the two. Command+Shift+Tab results in no action--it's not that the shift is being ignored, it kills the combo (i.e. Command+Shift+Tab does not bring up the application switcher, and pressing it while the application switcher is up results in no movement, not movement to the right). Furthermore, Command+Shift+Tab works fine on the built-in keyboard!

And while I was typing this I remembered something else: Shift+Tab doesn’t work either (e.g. to move to the previous form field) But it works fine on the MBP built-in keyboard!

What am I missing?
Sounds like a hardware problem based on the comments. Until you can try a new one, you could get the same action by using use Cmd+Tab (holding down Cmd but just tapping Tab) to bring up the switcher, and then use the arrow keys to go back and forward.

Or possibly the Karabiner keyboard customizing app will let you remap the left shift to something else.