For limited users, the edit search results display "You are not currently able to add notes to this edit. (Details)" at the bottom of every edit. The "Add Note" button does nothing except change the button text to "Delete Note" and "Delete Note" does nothing except change the button text to "Add Note".
If we need to display a message, I think my preference would be to get rid of the buttons and the message shown for every edit and display a single message at the top of the page saying the user is not able to vote or add edit notes.
If we don't want to do that for some reason, it would at least make sense to get rid of the useless button and probably move the message there instead (although we don't say anywhere on the page that the user can't vote, we just hide the voting buttons, so maybe just getting rid of the message would work too...)