After a longggggg time, this has finally been resolved for me by a tech support person at Apple. All it took was being a little more thorough. Hope others have resolved this problem by now as well. If not, all it took for me was:
1. Click on Finder
2. If you have "yourname" with a house icon next to it in your favorites, click on it, if you don't have that, you need to:
1. Click on Finder
2. Click on Finder on the top bar
3. Click "Preferences"
4. Click the "Sidebar" Tab
5. Check the box under "Favorites" next to "YourName" with a house icon
3. Click on "Library", if it isn't there, go to the top bar and click "Go"
4. Hold down the "option" key and "Library" should appear
5. Open the Library and open the Preferences folder, look through it for anything that has Twitter in it. For me, it was a com.apple.twitter.plist or something like that.
6. Drag that to the trash
7. Restart
Hopefully that solved it.
If not, try looking through your "Preferences" folder in the Macintosh HD->Library->Preferences and deleting anything with Twitter. I would also look through (In the YourName Library) the "Application Support" folder, and the "Caches" folder. One more thing, try deleting (In the YourName Library->Preferences) "com.apple.appstore.plist." and "com.apple.appstore.plist.lockfile"
I think that's about it.
Good luck everyone!