Of course the county should note any changes to the index. This not only protects the searcher but also the county.  If they do not report any corrections then the county clerk is a "suspect" anytime a searcher is accused of an error. 

 The county I work in makes a notation of any corrected error and the searchers watch carefully to be sure that they do.  

If they do not, any searcher accused of a mistake could, and should, suggest that any mistake might be due to an indexing error.