Unable to change the order of widgets in Yosemite Notification Center Today View
I was having the exact same problem, and I think it started after installing an app which included a Today widget.
I've finally fixed it by trying a few things, so I'm not sure what actually solved the problem. I suggest you try these things in the same order:


Open the Terminal (/Applications/Utilities/Terminal.app) and paste the following lines there, then hit [Enter].

/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/\
LaunchServices.framework/Versions/A/Support/lsregister -kill -r -domain local\
-domain system -domain user -seed


This will rebuild the app cache, which includes all extensions.
A few extensions will probably be missing now (in the Extensions preference pane). That is no big deal; just quit and open all apps that come with extensions. Logging out and back in would do the trick too.
Go to System Preferences > Extensions > Today, and reorder the items to your liking. Make sure you keep all checked items together and move them to the top of the list! I suspect the Today view could get confused when enabled widgets are mixed with disabled ones.
Log out and back in and see if the widget order is correct.


Hopefully, this approach works for you too.