Block Settings not applying to Zen sub theme
I solved the problem, but don't know exactly what the issue was.

While troubleshooting, I noticed some Warning 


  site:drupal.org Invalid argument supplied for foreach() in
  element_children()


As well as the tabs not changing names regardless of which themes were enabled. Disabled and uninstalled all of my custom modules, but nothing changed. Disabled and deleted all the custom themes I had installed, and the errors disappeared and the Block Settings menu started behaving properly again. I copied all the themes back in, and it's still working properly, so I am not sure what the problem was.

I will be reinstalling several of the modules and checking to see if the problem reoccurs, but for now all is well.