Why does my desktop picture not change correctly?
Open Finder and press the keyboard combination: ShiftCommandG
From the "Go To Folder" popup window that appears, enter the following bolded path (just copy and paste it): 


~/Library/Application Support/Dock/desktoppicture.db


Move the file to your Trash. 
Log out of the account and log back in. 


Explanation:
There's no property list for Desktop settings in Mavericks, as there was in previous OSXs. Instead, the Desktop values are stored in the database file mentioned above, which I assumed (correctly, here) was corrupted. Deleting it is non-destructive, as it automatically regenerates once you log out and log back in.