What mental illnesses cause different performance on the Wisconsin Card Sorting Task
The diseases and mental dysfunctions that have been studied are Parkinson's disease, Huntington's disease, ADHD, Substance Dependence, Autism, Multiple Sclerosis and Schizophrenia (with and without tardive dyskenisia). I'll add more specific statistics (such as trials required to acquire first rule) and better references later.

In the meantime, during my search I found this really quick table:
 from this paper showing the amount of completed categories and preservative errors (when a person is ignoring that the rule has changed).