I did some character art based how Tyrion Lannister appears in my head, as I’m reading the books. Of all the characters, he probably differs the most in the show. Peter Dinklage is great, don’t get me wrong, and his voice is absolutely perfect. He’s just too darned handsome.
I should note that in my reading, I look a liberty of my own. (spoiler) The book says that Tyrion has half his nose cut off, but it doesn’t really clarify which half. I though it would be much more grisly a face if the top half were gone.