Icons stuck on Desktop
This sounds like you have messed up your permissions.

To restore them  use the 


  Make sure that all the permissions are correct on your home folder.
  You can use the ACL tool on the Recovery HD to do this:
  
  
  Boot into the Recovery HD using ⌘R.
  Run resetpassword in Terminal (available from Utilities → Terminal).
  Select your account from the drop-down list.
  Click the Reset button for Reset Home Directory Permissions and ACLs.
  


Source: grgarside: https://apple.stackexchange.com/a/110346/

Unfortunately this method does require reboot.