Here how I repaired the bugs in Notification Center
After posting that Terminal command fix, the rep and I worked on the Notifications issue. Although both Notifications and sharing bugs seem to glitch at the same time, the Terminal command patch didn't fix the Notifications issue. The rep had me do something very simple next. Frankly, I am embarrassed that I forgot about this fix.
I rebooted into Safe Mode.
Restart your computer and hold down the shift key when you hear the restart sound. You should see your Mac display a thin progress bar. Keep holding down that shift key until you see "Safe Mode" on the top right of the screen. This will be a slow process. (It was for me.) Be patient. Your Mac is fixing things and restoring many settings, permissions, etc. back to default.
Log into your account. Your Mac might be sluggish. This is normal. The screen may glitch a bit. This is new with Yosemite. The rep was as surprised as I was. Once I was into my account, I tested the Notification Center and saw that all installed widgets were displaying and the items list showed all uninstalled widgets. Sharing services were also still working.
I restarted the Mac without holding down the shift key and logged back into my user account. Notification widgets remained fixed.
I can't attest this is a permanent solution since it's only been a few hours, but this is what Safe Mode does. It fixes things. The rep hypothesized that there may have been some directory damage or a file not configured properly during the install of Yosemite. Give it a shot and let me know if it worked for you, too. As of this moment, Notification Center works perfectly. (Well, except that Weather widget won't stick to where I want it to be. But I didn't want to be on the phone anymore to fix something so trivial.)