I found this article about Kenyon Martin's speech impairment. This came up in the thread about the April Fool's Day prank involving Kenyon.  Many people responded that Kenyon was out of line and that quite possibly his outburst was related to him having Tourette's syndrome.  I did a little Googling(is that a word?), and found the following column from the Seattle Times from 2005, where he discusses his stutter in some depth.  It mentions that the blinking and head jerks are a part of the stuttering issue. I think it's very insightful and may help put to rest the some of the confusion.  And, Kenyon's response to this difficult challenge makes me respect and admire Kenyon even more. 

http://seattletimes.nwsource.com/html/sports/2002158286_allen23.html