In Outlook 2011, is there some way to assign keyboard shortcuts to specific categories, so I can categorize messages without having to use the mouse to select the drop-down from the Categories menu in the Ribbon?
Yes, you can do this.
For some more ideas about how you could add keyboard shortcuts to Outlook:Mac, check out "Unleash new uses for keyboard commands in Outlook for Mac" in the Office:Mac Help Blog.
I had mixed results with the above method. It would work once, and then just scroll to the last email received in my list after that. However, I launched Automator (in Applications folder) and created a service (looks like a gear) from the new workflow menu. From there it only took 2 actions from the several Outlook choices included in Automator:
Drag these items to the workflow area and select the Category from the dropdown. Save and and name this workflow. Then, select Services > Services Preferences... from the program name in the title menu, scroll to your named workflow and double-click to the right to assign a keyboard shortcut.
The only downfall is that this shortcut will work from anywhere, I will try to isolate it to work ONLY when using Outlook later.