Although there's plenty about Mr. Grin to be intimidated by, there's nothing quite as frightening as his namesake grin: a scar running from the ends of his lip in the shape of a smile.
In popular culture, this is commonly known as a "Glasgow Grin." Supposedly invented in Glasgow, Scotland, the scar has been made famous by fictional characters like the Joker from The Dark Knight. And just as with the Joker, Grin's Glasgow Smile provides a fitting symbol for his sadistic nature.
As Mr. Grin attacks Alex, the young man gets "the impression that behind his livid scars he really was grinning" (12.42). By twisting this symbol of violence into a symbol of pleasure, Horowitz is emphasizing the difference between Mr. Grin and other violent characters like Herod Sayle and Yassen Gregorovich. While they use violence to reach their goals, Mr. Grin uses violence simply to make himself happy. It's a creepy difference, for sure.