You don't find it unrealistic that mat, with hundreds of men's memories (some very highly educated), wouldn't have some innate understanding of spelling? You don't find it unrealistic that Mat, a man who is completely fluent in the Old Tongue in both oral communication as well as the written word (he has no problem discerning the script on the ahanderei) can not spell in the New Tongue?

Mat is not one for the scholarly arts, true, but his experiences give him advantages that compensate. At worst, Mat's association with writing is best exemplified with his letter to Elayne and Nynaeve in Ebou Dar. Short and sweet. The less he has to do with writing, the better.

Frankly, I find it hard to believe that Mat would write elaborate character profiles, let alone a lengthy rant to Elayne.