I know that the movie Mouth of Sauron didn't really fit Sauron's description him but I get such a kick out of the character in both the movie and the books. I think that that PJ made him blind to emphasize the contradiction of his character. He takes himself sooooo seriously and yet he really is nothing more than a mouth.
Another interesting thing is that although the movie Mouth does not have eyes, he recognizes Aragron and Gandalf immediately. So in a sense he still does have that moment of intense eye contact with Aragorn but it is in a much more figurative way. He seems to be searching Aragorn's very soul; searching for a weakness that he could use to his advantage.
Creepy *shudders* The character in the books is much more intense. I found the movie character to be - forgive me - funny