I will list some major problems I think the SK has.
If there is an SK in the game, Town has too little influence on which people die. In a day-nightcycle, only one in three deaths will be caused by Town voting, which I find too few. Moreover, I think that the SK has too much influence. If he never targets Mafia, it becomes almost impossible for Town to win, and if the kills Mafia, Town can win without them having actually correctly spotted Mafia. This takes away many of the fun strategic aspects of the game. The best strategy for each individual player becomes to play in such a way to not get nighkilled, while this game should be about other things. Also, I din't think it is fun to hunt for the SK at all, or to play SK. Mafia can strategize with each other, the SK can't. Town can catch Mafia by discovering the way they work together, but the SK can't be caught in such a way.
All in all, I think the addition of the SK makes for a dumber game.